Nop is giving you terrific advice. I'm sorry that now is not the time to investigate spiritual options. I was a member of the Unitarian Church in several places I lived. I enjoyed it greatly and it is very nice for folks who are a little church leery. Unitarians are inclusive of many different ideas. Maybe it is something that will be doable in the future.
It does seem as if Nops list of questions is pretty basic if you are to decide what to do about the D. I hope your H gives answers you can work with.
Try not to take your children's preferences too personally. At different stages it is natural for them to have a preference for one parent over the other. It comes and goes. The tension in your household will tend to extend those stages. It is not a reflection of your parenting ability.
