brew - 'let him back', as in he's back in the house? or back together with you? for us, circumstances dictated staying in the same house, but i made it clear that this was not us back together - that would depend on progress with counselling and at home over time.
you're entitled to your hard feelings - and he as the cheater has to expect that to some extent. i think i wrote before, apparently average time to full recovery is something like two years at least... i have lots of hard feelings 16 months on! if your H is not showing remorse or bending over backwards to show you he is sorry and remorseful, and that he really wants this to work, that won't help you at all in your recovery (imo).
are you in separate rooms? if you are not sure about whether you even want to try staying together, you may want to keep your own space for now. Or... he needs to get his own place but come over to help with DDs regularly.
(And yes, realistically, it's very easy for people to say ltb, and don't worry you can take care of the kids, but in real life it's harder to do, and the thought of being a single parent may not be for you and therefore motivation to work harder at staying married).