You can (and should) cross add the key cards as well.. This way you only have to carry one card with you and you get extra spares to store.
I also recommend naming the cards in the UI.
I would first try signing out and then back in to the Tesla app on the phones.OK, we have both cars, my Y and my wife's 3. Tesla asked if we want to merge these accounts and I said yes. This request was to be able to access both cars on my phone and my wife's phone. However, swiping left on the open app only gives me an advertisement for solar power. Swiping right doesn't do anything.
Is there a special process to cross add the cards or just the same normal process in each car one at a time
Nothing special, it just works. As I previously noted, it is helpful to label the cards in the car UI.