I hadn't considered if existing legislation might already require implementing an age verification when l posed the question. Now that you bring it up, I fear it does.
The DSA has exceptions for small companies. But I would caution that there is no case law that supports your interpretation that users should be counted on a per-instance basis. Courts are often not very receptive to attempts to avoid rules through such formalities. Bear in mind that the DSA is supposed to protect the "fundamental rights" of Europeans, which may not include running an instance.
Other laws do not have such exceptions. This app seems poised to become the required age verification mechanism, wherever age should be known. Either use the app or show you have something better.
In January, a Berlin court ruled that TikTok was in violation of the GDPR for not doing enough age checking. It's being appealed. It remains to be seen how much of that case will be applicable to the Fediverse. But there is a good chance, that even without new laws, age-gating will become mandatory through case law.
You could run your own family forum just fine. The problems start when you want to federate. Let me be crass to make the point. Say someone posts child porn and that gets federated to your instance. You think you can just declare that someone else's problem to avoid legal complications?
The way I expect this would work, is that instances would become responsible for who they federate with. If an instance allows your family instance to federate, they would allow your users to indirectly use their instance. We'll have to wait what lawmakers or courts do, as you say. But I think, federation would only be by manual approval after some sort of check for compliance, or maybe even a legal contract similar to how it goes in GDPR. Actually, such GDPR contracts might be required anyway, but who cares.