TL:DR - does it really matter if DP lets his kids walk all over him if we're not going to live together anyway?
Been with DP 3.5 years. We don't live together because we have five children between us and don't want to disrupt them: they've already been through enough with their parents' break up. Happy to wait until his youngest leaves home in a couple of years.
I keep noticing how much he seems to lack boundaries with his kids: the oldest regularly gets drunk and trashes the house, and doesn't seem to get any consequences for this. All three finish eating dinner, and don't even take their plates to the dishwasher, offer to help clear up etc. The oldest was furloughed in the first lockdown, and DP was still working full time from home, but oldest didn't lift a finger to help. We went on holiday together, and neither of his oldest washed up even once the whole week - they were 18 and 20 at the time FFS.
The youngest is the main issue: when we've spent time together with the children recently, she's been thoroughly unpleasant to my 13 year old DD, to the point where we've decided that we won't be spending time together with the children for the foreseeable future. DP says he's tried talking to her about it, that he's thoroughly ashamed of how she behaved, but that she's just denying unpleasantness and passing it off as "banter" 
Recently she kicked her older brother pretty hard in temper, and there were no consequences, not even made to apologise.
Anyway, I suppose the point I'm making is: if we're not going to be living together til his kids have left home, and we're not spending time together with the children...does it really matter much that he seems incapable of disciplining his kids? He's amazing in so many other ways: he spends a lot of time with his kids, and is a supportive, loving parent; he engages with my kids, and they really like him; he's attentive and loving; he never fucks around with mind games and is always reliable; he's funny and clever; we get on so well, often stay up til 2am cos we can't stop talking. And the sex is spectacularly good! I just can't help wondering whether his kids will always manage to impact on our relationship. Maybe I'm still just furious with his DD for being so vicious to mine, but I'm also pretty pissed off that she seems to be able to behave exactly as she likes with no consequences at all, and I'm catastrophising that she'll always have him wrapped around her little finger.