Stop. Just stop. The skids are there to spend time with their father. DAD gives knife and fork lessons. DAD fixes their meals. DAD cleans up after them. Yes, they're kids. HIS kids, HIS weekend, HIS responsibility. NOT YOURS. 

What would he do if he lived alone and got his kids for the weekend? All of the above. Next time it's his weekend, make plans for yourself and leave him to spend quality time with his kids. 

Well you imported this man and his messy kids into your peaceful clean home and now look where that has gotten you. 
 

I would sit all of them down, remind them of the house rules (especially your SO) and that if by "they don't come here to work" means they don't clean up after themselves then him and his kids need to find other living arrangements. 
 

They either follow your rules (as the bill payer and home owner) or they don't (if they don't then they have consequences including age appropriate punishment and / or removing their father from your home thus letting his kids run a pigs sty at his expense in a home he pays for) 

Put your foot down - all the way down - otherwise this will be a weekly disturbance which will rob you of your peace that you deserve inside your home. 

I know this feeling firsthand unfortunately 

Guage people by their actions and never be fooled by their words.

Stop catering to him and them.  Instead, instruct him on exactly what he will do, exactly the standards of behavior and standards of performance he and they will be held to, and enforce those standards.

"Stop right there. Pick up your mess. Never touch anything in this house and for sure in the  kitchen  unless an adult is with you."

If he cannot enforce those standards, his kids are not physically in the home unless daddy is with them and they are all under your direct hairy eyeball oversight.  If you are in the yard, they are locked out of the house and can sit their purposefully under performang under required to perform and behave asses in the dirt or better yet, do chores.

Let SO know that if he does not get himself and his failed family progeny under control, that they will all be purged from your home and your life.

Keep it simple.  "Do as you are told, or you will not be welcome in my life and home."  End of discussion.  Make sure that SO and his kids all have this message.

Defend your home and your life from their failed family crap.

I get the fury regarding the behavior of these under developed spawn.  Our early family life included SS being with his mom and I all of the time. He was a toddler.  He was at just about every event, happening, and gathering with his mom and I.  All of our friends were in his life.  We got near universal admiration for how well behaved he was, how well he communicated even as a toddler.  My college BFF would even grouse at DW and I that we were too strict.  Those same friends, when they had kids, rarely engaged socially or publicly with their kids.  When we would socialize with them either with just us and them, or in larger groups with other friends and their kids, it was all I could do to not correct their rude, ill behaved, non communicative, coddled, spoon fed (literally, and at ages entirely inappropriate to be fed by mommy and daddy), etc, etc, etc....

It is interesting that those friends all are not particularly close with their kidults.  Some of their kids are nearly incapable of functionign as adults, other of their kids are doing fine.   Those who were coddled under capable children but were held to some behavioral standards, are doing far better than the kids who were entirely coddled and did not have behavioral standards that they were held to.

"I just brought my house, not mine and he lives rent free and agreement is as I won't add to mortgage I pay for everything refurb wise but he will help with manual labour."

May I ask as to why this man lives rent free in your home? And gets to exercise visitation in your home?

I think you're being used.

Just a few thoughts and observations... there are some red flags here to look at.

1.  I actually agree with him about the "finish your plate" thing.. that actually isn't a healthy thing to do to kids.. there is a balance with not wasting food.. so maybe the lesson is that if you can't finish two pieces of pizza.. you take one.. eat it all.. then if you are still hungry you can have a 2nd.. next time the kid gets served ONE piece.. or smaller amounts.. and see about 2nds.

2.  The lessons in table manners.. that is for his parents to teach.. but isn't it a red flag that the kid can't do it?  what about his mom.. and dad.. that had him to raise for 9 years.. what kind of manners does your SO have.. do you think you have a man that perhaps isn't so refined and mannered himself?... 

3.  Kids absolutely can and often don't mind helping.  The kids should have been out there helping with the fencing.. because it is time with their dad.. they are learning to work in a team and get the satisfaction of seeing a good job done.. it is ABSOLUTELY the kind of thing kids should do with their parents.. you don't have to give them dangerous tools.. but they can tote boards or posts.. they can hand dad tools.. learn to level... etc..   It's also part of learning that you are part of a family.. everyone contributes.. and that way things get done faster.. then everyone can go out for a treat later.. etc..

4.  I still get the occasional paper towel.. eyeglass cleaning wipe or screws in my wash.. from my husband's clothes... I know.. people should be more careful.. but the real solution here is to have your SO do his kid's laundry.. NOT you.. (where he learns to clean pockets before washing).

5.  When you find these messes.. and the kids are still there.. you tell your SO.. that he and the kids need to clean it up.  that's it... if they are gone.. HE can do it alone.. maybe he will do more about it when he is the one paying the consequence.

6.. AND this is a big one.. why are you letting him live in your home for free?  hosting his kids for free?  I know he is not on your deed..  doesn't have ownership in the home.. but that doesn't mean he shouldn't be paying RENT to you.. and as your partner.. he should ALSO want to help improve the home.. because ultimately.. if you are going to be lifelong partners.. he will be getting the benefit of living in a nicer and fixed up place right?  and wouldn't he want to help his partner.?

The last one is really concerning.. why is he not paying rent.. can he not afford it?  again another sign you may have gotten a lower class.. no mannered mooch.

First of all I can understand you not wanting him to pay for house upgrades.  But everyone has to pay rent. You rent a apartment, a year later you don't tell the apparent management company you own part of the building.  SO must pay  rent. As a lease,  He gets to share a bed,  all the rooms for $X a month. 
'His kids are his responsibility, he cleans up after them. He is right  his kids don't have to work when over. You don't have to cook clean, Uber.  Buy food, clothes ect. For those kids. 
'This relationship is looking not good. If you are fighting about the small things,  That he thinks you should " mother" his kids ,  That his kids are your responsibility,  you have a serious problem.
 

Most divorce people , like all people want the  famous " HAPPY FAMILY ". They had there chance, it ended with the divorce.  They can not recreate it.    Because your Hapoy Family doesn't include his kids 

I have what might be a strange opinion about this type of situation. It's one thing to be the caregiver for his kids if he is financially supporting you and this is your arrangement. In a way, you would be "doing your job" in exchange for not having to go out and earn a living elsewhere. Same with being a stay-at home spouse and caring for the home. I've seen this work for some people.

BUT - if you are paying half (or in your case most of) the bills, this is not your job. His kids are his job and at their ages, they are unlikely to accept you as a parent figure anyway. I tried it with my SO's kids. I have kids and i always handled them with little trouble. I thought, "What's adding a few more kids, my kids aren't difficult for me so this will be fine."

It was not fine. SO's kids were not raised with the same values or behavior standards as mine (not saying mine are perfect, just different) and the younger SS actually hit and kicked me, and would just run off in public at age 9. It wasn't his fault, as he was raised differently.

I then refused to watch him because i can't be responsible for a kid who won't listen to me. SO has never paid my bills, either, so i am firmly disengaged and won't cohabit while kids are in the home. Your SO either needs to do for his own kids when they are present or host them elsewhere.

Funny you mention the knife and fork thing. I remember looking at SS now 14 and having to explain and demonstrate how to cut meat at age 10. His parents did it for him until then. He also couldn't tie his shoes and neither SS (14 and 20) can ride a bicycle. They have corrected their behavior to some extent on their own due to likely peer pressure, but they have been failed in many ways. We can't fix them once they get past a certain age and even if they are babies, unless they are with us fulltime, there isn't much we can do. All we can do is manage the extent to which we will allow our partners' parental failures to impact us. 

It is time for the choir to fire the breeder partner with the failed family baggage.

Re-read your OP and the comments.

Save yourself.  More importantly, respect yourself and stop letting this failed family spawn butt sniffing failure detract from your life.

Equity partnerships can take on various formats, there is nothing equity partnership like in your relationship.

Take care of you.

You have a lot of power in this current situation. Will you use it or not?