I moved in with DP, into his formal marital home last summer. We each have DCs. He earns a lot more than me so I'm kind of in the same position as your DP is with you. He owns 100% of the house we live in, and pays for any maintenance on it so I don't consider I have any financial stake in it. Bills, we split 50-50 though - just as we would if we were renting. I still own the house I lived in before, and have rented it out. DP is letting me keep all the money from this, which I feel kind of evens things out as he works much longer hours than me so I tend to do most of the housework, and also help out with his DCs quite a lot. If your DP doesn't own a house then presumably he'd be saving quite a lot in rent if he moved in with you? If he has enough money to buy even a small house, why doesn't he do this, and rent it out - then you will each have assets that are easily separable.
So separate finances seem to be working fine for us. And even though the DCs are quite a bit older than yours, they do understand that they have different parents and different lives to some extent. My ex is very hard up so DCs don't do expensive stuff with him, whereas DSC go off to posh places with their mum. Everyday stuff whilst they're all with us does need to be the same (holidays, clubs, etc) though you can retain separate finances and just decide that one of you is going to treat everyone to a holiday, or whatever - rather than pool money. Inheritance doesn't need to involve treating everyone the same though when they have different parents.
Re pre-nups - we're not (yet) married, but I think we'd definitely look to make one as best you can (legally a bit of a grey area still I think). When one or other of you has been badly hurt (financially too) by previous divorce, and has a lot more assets than the other one, and you both have DCS, you'd be silly not to really. Not romantic, but then neither are wills are they? Just a good way of reassuring each other that you're not marrying for money, and taking the stress out of feeling that you're risking everything you've worked for.
Re schooling - DSC are all in private. My DS is already happy and settled at state secondary, so won't be moving. But DD is Y5 and already asking if she can go to the private school that DSC attend. I'm putting off deciding, but at the end of the day don't really feel I can say no on financial grounds when DSC are all there. DP understands this and is willing to help fund it if necessary (plus he thinks it's a good school, and I guess wants the best for my DD too). I think if he wasn't willing to help with that, it would make me question the nature of our relationship.
But don't rush things. We spent about 9 months planning moving in together. And it was a fun time. But also gave us a chance to talk through house rules, parenting, finances and other things before we told the kids and took the plunge.