This short blurb tells a lot: DH “feels it's easier for he and I to take care of chores than to nag the kids.”  This tells me your DH likes to take the “easy way out,” which usually winds up down the road being the hard way.

Parenting is not nagging.  Things such as asking and expecting your kids to pick up after themselves and having boundaries, etc. is PARENTING.  It is NOT nagging.

Since your DH is, in essence, a lazy parent, he now has lazy children.  Unfortunately, no surprise there. 

Is this deal with 18 YO SD temporary or not?  She is an adult.  But, your DH has to be able to control and manage his own children.  He should not have the expectation that you do this.

Either stick with it or go all in. What I mean is everything left out for 24 hrs or more, EVERYTHING, gets trashed. Thus includes not only trash but dishes, clothing, crafts, etc.

If you want to hold onto it like dishware, then clean it when no one is around, then store it away from use. No one else cleaned it then no one else cares to have clean dishes or any dishes. This includes pots, pans, glassware. If things go away and you are asked, it's just, no idea. Personal things get trashed, donation, or just stored in away from use. I found that no one noticed this but YSD who stopped leaving her stuff out.

Let your DH buy replacements. You do not. As for disposable serveware, it will not solve the isse and will still be left out. So if this happens, take all that stuff and stack it in kitchen.

In any case I hope you aren't still cleaning the kitchen before you cook....I just refused to cook if I had to clean it first.

Pick the rooms you need to be clean for your own sanity, and pick up those. Throw any of the skids' stuff into their rooms and close the door. If you need a clean kitchen, clean that only. If you need a clean space to sit in, clean that only. But don't do anyone's laundry except your own and BSs.  DH can take care of the rest.

My SS was pretty good about picking up if I asked him to, will yours, or will they ignore it? Is a housecleaner an option for you?

I agree that DH would rather pick up after them because he doesn't want them to be mad at him, ie parent them. Does he care that you are unhappy?

Oh no.  If DH doesn't want to nag the kids to do age appropriate chores, DH can do those chores himself. His spawn, his problem.

Do not volunteer to remain the live in beck and call girl/chore bitch.  Make DH the primary chore labor pool, particularly considering that all four of the kids in the home are his while only one of them is yours.  The three Skids are far past old enough to have chores and suffer consequences for not doing them.

Since DH is the one choosing to not hold the Skids accountable, he can be the one to do the chores.

Keep it simple.

Something else to consider, you are the BM and if you decide to end this it is likely that you will be the CP and BioDad will be the NCP paying you CS.  As young as the baby is, ending it now and moving out of state forcing a long distance visitation CO into effect will significantly minimize the influence of DH's shallow and polluted gene pool on your baby.

Take care of you, take care of the baby.  Which very well could mean leaving daddy to deal with his older spawn on his own and limiting the baby's exposure to all of them.

We have a member who has two SDs and a lazy, conflict avoidant H who let his daughters trash the house during visitation. The SM asked, reminded, told, begged, and pleaded to no avail. Finally, she bought big trash bags and would do a sweep of the home. All of the crap the skids left lying about went into the bag, and then the bag was tossed out onto the garage. If his baybees needed a particular item, they or daddee would have to search through those trash bags for it.

Behavior modification accomplished.

Keep the strike going. I never clean up after them. DHs divorce house is trashed but oh well. Over the last year SD has actually stepped up and started picking up after herself and doing the dishes after dinner. They eventually come around when they realize no one will do it for them. 

Im not defending your DH or SKs at all but wanted to share a long-term perspective.  I'm a 75 year old BM & SM of 5.  They all lived with us, plus many pets.  I'm not a ball of fire but tried to keep the house livable.  The kid's rooms were often messes, i'd just shut the door.  The kids were typically adolescent like yours.  I had cleaning help once in awhile.  To be honest, we had some big glaring issues that took precedence.

Flash forward, they are all in their 50's.  SD is a spotless housekeeper, you can eat off the floors.  OSS is average but things look fine.  BS is tidy.  BD is "artistic", "bohemian" but it's good enough.  YSS can only be described as fanatically clean.  I guess what I'm saying is do what makes you feel good but they will probably be fine as adults.

I told my husband that hemake his lazy pos disrespectful and selfisg son who was 17.5 yrs old, pick up after himself. He empties the trash, kitty litter, his dishes everything he cleans.

he had the nerve to tell his dad that this is my job as a sahm.. wtf?? Your own mum never cleaned the house but suddenly its my job?? 

My husband told him it was not my job to clean up after a lazy kid and as i had a newborn, ss doesn’t dump his messes on me... I remember when my kids could crawl, ss would leave skewer sticks from take out on the floor. Know how I handled this laziness of him not emptying the trash??

i told hubby that if our crawling inquisitive toddlers injured themselves with ss’s plastic forks or bamboo skewer sticks that he dumped on kitchen floor or our cats injured themselves because of it, i’d jam that skewer stick up his pee hole and he’d cry like a little inconsiderate biatch!!

hubby put an end to that immediately. Sarcasm is the only way my husband puts his foot down because he sees how inconsiderate and selfish ss is...