First, it sounds like the cats were jointly owned rather than truly "your” cats. Pets are generally treated as property under the law, like a car, TV set, toaster with the notable exception that there are laws to prevent cruelty and mistreatment of animals. The amount of time you spend with something does not determine who owns it. If the cats are co-owned then she had as much right as you to take them with here.
A court is not going to get involved in resolving the dispute over who gets the cats until one of you files for divorce. Then the cats will be treated as part of the property division in the divorce. That won’t be a fast process unless the two of you come to some agreement about what to do with the cats. While a court might consider some kind "visitation" order while the divorce resolves who gets the cats, that is not common and in any event not likey to last beyond the divorce process. A court is not going to want to retain jurisdiction over a divorce case to deal with visitation issues over cats. Rather, especially since there is more than one cat, the court is most likely to simply to divide up the cats between you, e.g. you take Fluffy and she gets Mittens.
If you really want to pursue getting the cats, get yourself to a family law attorney and see what you can do in the divorce and to get the process started. Until you get the divorce started you won't get anywhere.