"with her covering his self-employment tax shortfall"

Uh, what? Any payroll withholding is part of "their" tax payments. If they are not withholding enough + not also making estimates, then there is shortfall for Taxes, but it's not exclusive to any one tax type. And if there is a refund, is that only hers?

MFS is not the way to resolve a fight over whose money in a marriage is supposed to pay for which things.

And it seems they need some help with prepayment planning.