With hindsight, it was probably a bad idea to have your gf move in with 2 kids, especially in light of the fact that she and your kids were alone together for long spells every day.   Had your son and daughters seen much of your gf and her sons before they moved in?  If not, it may have been a real shock to them to have these 3 strangers move in with you.  Blending families is tricky at the best of times, but the circumstances would have added extra strain, I think.  Have you talked to your son and daughters about it at all?  I wonder what their perspective is. In answer to your question, yes, sadly it is common for kids to make a new partner feel unwelcome!  Just ask anyone here ;-) 

If you read the blogs on this site, you will find many instances of "step-issues" that cause partners to run or want to run. I would suggest reading through them and seeing if anything sounds familiar. Without any further details, that's the best i've got! 

I had some idea of what I was getting into before SO and SKs moved in. They both had thier issues but SO and I had a strong relationship and at the time, with structure most of thier issues were tolerable and fixable. I'm not a judgemental person and am fully aware most kids especially those from divorced or separated families have adjustment issues. But at the time SKs and I had a good relationship and there was respect. 

I never anticipated the PAS from BM that would eventually occur simply because she had minimal involvement in thier lives at the time and the turmoil that would follow. 

First of all, it was a bad idea to have these 3 strangers move into your house at all, while between houses.

I'm a big believer that you don't move in with a partner unless both of you are truly committed and plan to be together forever.

I agree with the above, it was a bad idea and apparently, your kids thought so, too. Three months is a long time for guests.

Unless you deal with your kids now.  You will never have another relationship with a SO.  Your kids now know they have the power, and control to push someone out of your home .  They will play this everytime you have someone 

Moving in a GF or BF without papers and without setting clear boundaries and expectations for kid behvior is a recipe for exactly what you have experienced.

This is likely not entirely on you and your kids, your XGF brought her kids to the mix as well.

Next time, have papers before you move your mate in. That gives you something to roll up and smack any kids who cause a problem around the head and shoulders with when they choose to violate the standards of respect you demand from them for your mate and your relationship.

Don't lament what is lost. Embrace what you have learned so this does not repeat the next time you find someone.  Kids need to understand that daddy and mommy have a life after divorce and beyond them (the kids).

Good luck.

Not worth the effort.  She, for whatever reason, has ended it and moved on. Do the due diligence of introspection and see what you and your own kids may have done differently so you don't repeat that behavior when you pursue a future relationship.

Kids can sabotage a parent's follow on relationships in a heartbeat and .... a parent can sabotage their own relationship by prioritizing their kids over their SO.

Don't do that. And don't let your kids sabotage your life.  Be their dad, they are not your life partner(s).

Recovering the relationship with your recent X is so unlikely that it is not worth the likely pain it will cause you both.

Good luck.