AMEX Platinum.Unlimited, yes, but only for cardholder (or +1). That's not useful for a couple + children.
Depends on how often you travel, I suppose. But if it is just you & your wife, cards with unlimited visits for cardholder +1, like Citi Prestige, may be more suitable.
Husband main holder + 1 kid.
Wife supp card holder + 1 kid.
PP unlimited 1+1.