If it is absolutely killing you that you get to see them so little now, and you'd like that to change, then there is only ONE WAY you can improve the situation.
Stop with the shit about feeling that somehow she's ripping you off. She isn't. It really, really DOES NOT MATTER in a family where one parent is SAHP who earns the cash. The whole set up is predicated on the fact that the parent working can fly high, achieve those career ambitions and AT THE SAME TIME have that lovely family life... because the other parent faciliates it.
For every sole earner feeling they earn it all, there's a SAHP resenting the fact that they've lost out on their career and pension and network because they gave it up to raise the joint kids.
YOU WERE A TEAM. You took decisions as a team. It was never your money any more than they're 'her kids' and not yours because she devoted her 'public/work' time to them and you didn't.
If you can manage to keep that mindset you will honestly, honestly end up happier. So you are funding the team still? Well yours was the earming power that the team built up, so yes. Eventually that will change, spousal maintenance won't be forever.
If you worked full time, even from home, she'll know the vast gulf between the level of involvement you feel you had and the reality, so to throw out that you could easily have them full time is just inflammatory. And the au pair comment -! The kids shouldn't be with you full time because she's their primary carer, always has been, and that MEANS SOMETHING. You can't have it all. You can't be the full time worker and also see yourself as 'just as much' a practical everyday parent to young kids as a SAHP. It just won't be the truth, any more than she could stroll into your home office and say, well, I could do this while they're at nursery, what's the point of you exactly?
If you can genuinely stop with that gut feeling that the finances of the team you built should now be 'yours' then you will see a difference. Similarly, she will be grappling with the gut feeling that your joint children are hers. You both need to realise that your team won't be disbanded for many years to come, if ever.