In a compromise, each person gives up something such that everyone involved suffers ‘fairly’ and ‘equally’. A genuine solution, on the other hand, is one which everyone involved prefers, including preferring it to their own antecedent preference. No one is suffering, ‘fairly’, ‘equally’ or otherwise.
Does the proposed solution spark joy? Is everyone beaming? Are our eyes all shining? Do you see delight? Joy? Animation? Skipping? The odd cartwheel, perhaps? Is it a “YES!!!!” all round? That suggests you have created a real solution.
We look at our respective reasons for wanting what we initially want, and we create a way to proceed that we all prefer—a new idea that did not exist at the outset.
Ultimately, we all (including our children!) have to do what we ourselves think best, what feels right to us ourselves, not what someone else says is right. We are all moral agents in our own right. When we self-coercively override our own wisdom and do what someone else thinks we should be doing, we are acting wrongly by our own lights. No good can come of that. Treat this site as a source of speculative guesses and interesting arguments, not as an authority you should obey.
Taking children seriously involves not just solving obvious problems when they arise, but thinking about and experimenting with different ideas about how to make life even more delightful.