This is probably more difficult a relational problem to solve than getting access to her garage door opener so you can park out of the rain when you are visiting her. Presumably your cat can smell her cat on you after you've visited her, and vice versa. Each cat knows the other one exists. Assume you try bringing your cat to her home. Better chance that the cats will stage a spectacular fight, chasing each other all over the place, hissing and spitting at each other.
Cats are extremely territorial.
At minimumthis will require a his and hers cat box, as well as separate food dishes. If this does not work, consider selling both your homes so you can move both cats into a new house. That way neither cat will have a priority claim over the other to the house. One way to avoid really serious problems is to start training your cat to sleep on the opposite side of the bed from her cat. This will likely require purchasing a much bigger bed.