I think you need to sit down and think about how, in an ideal world, you can protect the kids from what seems the inevitable split. The relationship sounds, bluntly, horrible and I couldn't live like that - so really I think you need to think about how you can share time with the children, and provide two (ideally) adequate homes for them, with the resources - financial and time - that you share.
You say she's very academic - does she earn a reasonable wage? Do you? What sort of equity do you have in the house, and would it found two flats, perhaps, on each of your salaries - or if you rent, how can you both manage a deposit on new places that could home each of you and the kids? Is it feasible for the family home to be kept for one of you, with the other person able to have somewhere? Those sort of practical concerns should be uppermost given there is no relationship to save. If her career has been harmed by having children, in fairness that should be factored in - as, in the far rarer times where the father has been primary carer, should his own career hit. That sort of thing needs to be considered fairly and a path forward found.
I'd absolutely agree that some couples counselling is needed, even if it is just to help you communicate better as you split up. The children will be desperately harmed if this is a vindictive and high conflict split, but it sounds as if your relationship is going to harm them if you stay together, so splitting up as constructively as possible needs to be the focus.
Quite honestly, and this isn't unusual, all the attention is on the adult relationship. If it's this dead in the water, the focus needs to shift to how you can best protect the children from the adult mess, and how you can rebuild a new life, both apart, that meets their needs.