I'm going to try to zoom out and go into the vision of what I think is important and I try to not dive too deep into the specific implementation. I like how Job structured his answer so I'm stealing his approach:
Couples without kids:
I would like to see legally shared bank accounts which cannot individually be cancelled by either partner. This also implies each partner having their own name on the bank card. Accounts created can either be shared, but I would also allow partners to create accounts which are private. This set-up guarantees both couples who want to share all budgeting and couples who value their own financial independence but who also want to share some budgets can use bunq.
It would be quite useful to be able to see who made which expense from a shared budget, by setting a PIN per account holder (simple also offers that: https://www.engadget.com/2016/09/29/simple-shared-bank-accounts/).
Couples with kids:
Same as above but then with the addition of a new account type: a child account. The child cannot see the parent's accounts and the parents can see the child account(s). Parents should never be able to see the child's balance and transaction history, nor be able to transact money from those accounts and children should enjoy as much of the feature set as possible.
It's important to give families enough accounts so the kids can experiment with budgeting/saving. I think this is one of the core strengths of bunq and which you would want to reinforce.
Kids can order maestro cards or mastercards, but parents approve the request (since they are paying for the subscription). Once the child owns a card, they can do exactly the same thing any user can with their cards (attach secondary account, block, etc). Kids should have their own name on the card.
As a child I would have loved a more customized bank card and ideally you give them the ability to personalize their cards. There are probably some legal issues here (ING will have set these rules for a reason: https://www.ing.nl/particulier/betalen/passen/afbeeldingsregels-mijn-betaalpas.html), but with some pragmatism and by making deals with brands, I'm sure you can offer customized bank cards which are appealing for kids.
Bunq does not pay any interest. However, I would love for children to find out about the benefits of frugality and if I was a parent I would want to stimulate that. I would want to be able to set an interest rate and on a monthly basis the kids accounts would receive interest payments on whatever amount they have in their bank accounts. The interest payment is taken from a parent's account.
Conceptually I would approach the family subscription as a way for bunq to be relevant for families (upsell) and to build up your future customer base (similarly, I believe bunq should offer students the premium subscription, minus the 10 free withdrawals for a reduced rate asap).
If you start limiting the feature set for kids, then you are not preparing the kids to be customers. Their main association with bunq will be that bank which allowed their parents to limit them and spy on them. I believe bunq should not be used to give parents more control over kids' lives. The goal of giving children a bank account should be to have them experiment and make mistakes in a controlled manner, where the control is exacted by the amount of money a parent gives them and not by keeping a check on how they spend their money. If kids withdraw their money from an ATM, parents also have 0 control.