Should be able to. As per what I’ve read and understand from the past few posts here. As long you use a different bank’s card (not different card but same bank), then it’s fine. Just “clock in” using your and your wife’s boarding pass will do for your 2 teenage kids. In total you’ll need 4 banks.
Bank A - yourself
Bank B - wife
Bank C - Teen 1
Bank D - Teen 2

Mind you that each bank n card usually allow only 1 time entry per 3hrs usage. So dont think of you can use Bank A for you + wife/teen.