I would not recommend any Madrid Card for a family visit.
They are expensive to buy, kids don’t get discounts, and their validity is limited to a few days only. As you find out more about what could interest your children in Madrid, you will realize that a buying Madrid card does not make economic sense.
Children enter attractions for free
Most Madrid attractions will allow children under a certain age to enter for free. And for older kids, even for teenagers, there will be discounted entry. So a City pass will actually end up being more expensive to use for kids anyway because it is not discounted.
Most attractions are clustered together
The major attractions of Madrid are all close to each other so an unlimited transport pass does not make sense because you will soon realize that walking across is quite simple, and Madrid is a child-friendly walkable city in the historic center.
With kids, plans can change fast
The economics of the Madrid city pass work only if you see many attractions during your visit. In my experience traveling with kids is never predictable and you may see yourself canceling your visits to some sights or spending longer than you planned at other. So the money you pay for the Madrid City pass may not make sense.
So what pass makes sense with kids
If you see yourself using a lot of public transport in Madrid, buy a shareable transport pass, the Metrobus pass for 10 rides. In any case, toddlers and young children under 6 will travel for free and the rest can share the rides loaded on the ticket. In my view, this is the only pass in Madrid that makes sense for a family visit.
Also, in my experience, I recommend for families to take taxis for short distances if you don’t walk to walk; this works better than waiting for a bus or metro with small children who may get cranky. A taxi is instant and for a family of 4, it can be quite affordable in addition to saving time and keeping the family peace.