I'm not 100% sure that will work exactly as you want, but it might be a first approximation to try out, maybe. You could install the same wallet, with the same seeds (use the same 12/24 words) in all four wallets, and make it a multisign wallet so that each member of the family has a hardware signer of which two (of the four) are needed to sign transactions.
Yeah I am not totally sure what I want is possible. I wonder if its just a matter of wallet UX or if there are any technical limitations as well. This is probably where all those managed services like Casa come into play.
Another structure I thought would be interesting would be one where each individual has an "account" that exists within the main wallet. The idea being that they can send and move funds out of their "account", but no access to anyone else's funds. However, the wallet would show the sum of all accounts and if enough "accounts" agree then funds can be spent out of the main wallet directly.
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