If you were married for all of 2023, the community property rules apply. If you file separately, you should generally each report half the total family income (you report half of her income and she reports half of yours), you each report half the deductible items (regardless of who pays).
You don't really have a choice to have only one spouse claim the mortgage and only the other spouse claim bank interest. State law controls how you file, so see a CPA in your state if you aren't sure, but you really need to reporting everything 50/50.**
If you agree, you can "divide" the children any way you like. You are correct that if you can't agree, the tiebreaker goes to the spouse with the higher income. But if you agree to claim one each, that's perfectly fine, the tiebreakers only apply if you can't agree.
You should file a correct return that reports half of everything regardless of what you think your ex will do, if you file separately, then any mistakes or problems with her return that don't match your return are not your concern.
**In some cases, some property and income might belong to only one spouse instead of the marital "community." For example, if you owned a rental house before the marriage, and you have continued to rent it out and manage it, then it might be your property only instead of community property. The same might be true for retirement accounts and investments that were solely owned before the marriage (but not new contributions or investments after the marriage.). Again, this may require a CPA to untangle.
