If both sides follow the psak of a beis din for all matters, monetary, visitation etc….then whatever the decision, that is the halacha. Unfortunately, on both sides, the parties go to beis din for the items that suit their needs and the courts for those that dont.
We made our beds, now we must sleep in them. If we dont like it, we must remake our beds. Respect for batei din in general and rabbonim in particular (or more precisely the lack of it) is the root cause of all these problems.
There was a time when a Rav or beis din issued a psak and those who flaunted it were looked down upon, now when someone gets a psak they dont like they just look for a new Rav or beis din and the gabbai gives him shlishi in shul the next shabbos.