Two things... I'd call the credit card company and make sure you inform them that you will not be responsible for any further purchases made with joint cards. Get something in writing (an email) clarifying how you are dividing the debt, because, otherwise, if you pay down your half of the debt, you might be stuck with half of the rest of it, too.
We had two credit cards, with about $28K total debt, $20K on one, $8K on the other; I got a new card, and and let the existing CC companies know I would not be liable for any additional purchases. I sent an email to the W saying I would like to use our tax return to pay down the cards so there was an equal balance on each, and suggested she continue to use one existing card and pay off the new existing balance, and we close out the other, and I would pay off the new existing balance on that one. She emailed back saying that was a good idea. Now the balance on each is about $4K, with the pauper's share going to the card she was going to retain. She apparently misunderstood, and thought we were going to split the tax return in half, and she'd be left debt free on her card, and I'd still be stuck with $12K of debt on the other one. Only having her agreement in writing prevented it from being contested in court.
The other thing you have to remember is "time is your friend." You may reconcile and rebuild your marriage. But you will never get your marriage back again if you keep up the pursuit. How has that worked out for you so far? All you are doing is driving her further away. It's time to do something different. She needs time and distance to remember why she loved you. It's so hard. We're all going thru the same hurt, and we can all relate.
M:23 T:26 Me:53, Wife: 60 S:18 D:16 filed 7/16 W moved out 4/28/17