As @splasher noted, this is a bank problem, not a quicken issue. I suggest you contact the credit card company, close one card and add a second user to the remaining card. Tell them what happened so you can be sure to keep the card with the highest credit limit and get separate user ids both associated with the same card. Once up and running you can hide the quicken account associated with the removed card.
The above would be the recommended above board way. Another more straightforward, but probably not what most would recommend, is to cut one card in half and just use the same Id for both of you going forward.
How do you propose to get the credit card company to accept a single payment and split that between two separate accounts?
I've never known a comapny that allowed that to happen.
Getting it to look like that in Quicken can be done with a split, but that doesn't get it done in the real world.