I think the resentment would kill you the way you describe it and your children would also fare very badly. I too don't understand how your boy and girl are supposed to be accommodated - at all - if, in a 3 bed house, his 2 girls have a bedroom each. As for an 8 year old and 6 year old "refusing to share" ..... well, that doesn't bode well. The children are all of an age where the adults get to decide what the house rules and arrangements are ..... so if this "refusal" to share is being touted to you, that makes me think that your DP is already prioritising his kids over yours.
I didn't read this as being about "losing tax credits" (plus sceptical face ?!) .... I read it as being about a woman who, sensibly, does not want to lose her financial independence - which, given the whole job/school considerations, plus the tax credit issue which can't be conveniently ignored if childcare has to be paid for (you can't live on thin air if all your pay goes out again on care) - would almost certainly happen. There's nothing wrong per se - obviously - with being a SAHM, but no-one can dispute that it's the ideal situation for all women and there's a big difference between choosing to be a SAHM and having the choice, in effect, made for you because you can't otherwise earn enough to clear any pay once childcare has been sorted.
Even if OP did move in with DP it sounds to me like her and her children would have to sacrifice a great deal given there can be no compromise with where they live due to DP's job. Even if she accepts being a SAHM and living frugally - it sounds as if her children would either have to change schools or spend more time travelling to their existing school every day.
Given how hard it can be to blend families anyway, I don't think the OP is being unreasonable to be pragmatic about this. How awful would she feel if she moved in, became a SAHM, but the relationship later broke down and, by then, she'd been out of the job market for ages. How bad would she feel about throwing away the good job she's got lined up ? .... these days, it's a very big thing indeed to dismiss a good job. And where would that then leave her children ?
I really think in the circumstances you'd be best to remain apart. As Bogeyface says this would also give me food for thought anyway - it's not just about being able to afford to do nice things if you live separately - it's also his attitude which seems less than welcoming based on what you've described so far. Reads like you and yours have to fit in with him and his, rather than him proposing compromises and possible solutions to the living arrangements - still can't imagine where your kids would go !
Oh - and of course, you'd be particularly vulnerable as a SAHM if you're not married in the event of a split.