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SurveyJS
Open-Source JSON Form Builder to Create Dynamic Forms Right in Your App. With SurveyJS form UI libraries, you can build and style forms in a fully-integrated drag & drop form builder, render them in your JS app, and store form submission data in any backend, inc. PHP, ASP.NET Core, and Node.js.
At one point I seriously considered self-hosting a Rocket Chat [1] instance for very similar reasons. It seems to have a good balance of features, moderation controls, and polish while still being pretty straight-forward to host.
The main challenge I ran into was, of course, convincing folks to use it (instead of the "easier" forms of communication that they already had....).
1. https://rocket.chat/
Jami (https://jami.net/) has the advantage of keeping your child's communication private and lacks the ability to find outside groups (like phone calls), while having the features they would want to have to interact and being multi-platform.