They are possibly the last thing on his mind!
Sorry if my words come across as harsh, OP - but he has every intention of looking out for himself first and above you and dd.
He's had no problem spending family money - which you help earn in your role as sahm - on OW.
He's had no problem point blank lying to your face
He's had no problem with sinking to the depths he has regards deceit, betrayal and breaking the moral code
He will start fucking about with the money once he realises you are serious about not doing anything for him.
"well if you're not my wife then i don't have to support you" or some other lame excuse like that.
Remember - he could easily open a new account and get his wages paid into there. Then what would you do?
You can't trust him one bit.
You can't assume to know the inner workings of his fucked up head.
The one thing that you can bet 99.9% on - he will put himself first.
Transfer half the joint savings to your own account!
Do it the same time you cancel the other card.
Don't tell him - let him do his own donkey work.
The way he's been able to compartmentalize his two lives, txt her 'openly' right in front/next to you....all whilst playing at happy families with you.....it's creepy, quite psycho actually