My mom's cat doesn't like my cats

Most cats are much more territorial than dogs are, believe it or not. They will play together only in space that they accept as shared territory. Very careful introduction, usually over a week or two (or longer) can convince them to accept each other, but only after a lot of posturing and threatening and so on.

Not really recommended unless they're going to be sharing space for months. It's more stressful for them than the convenience for you is worth, and they won't thank you for it. Leave them home next time; they really don't need a play date, and definitely not with their grumpy old aunt.

If one person is only occasionally cat-sitting both sets of cats, the best solution may be to continue to keep them physically separated... I'm not sure whether meeting on neutral ground would make the process easier or harder.

Your mother's cat is very possessive. She thinks of your mother's house as if it's her house. It's her territory. She is the only pet there. Will you be happy, if someone - a stranger - comes to your place without invitation and lives there for 2 weeks? I don't think so :) What you must do is:

• Don't let your cats meet with your mother's cat meet in first day when you come. Close newcomers in one room, but try not to prevent you mother's cat walk where she wants. She needs to feel herself comfortable. She is at home, your cats are guests.

• Next day let them meet but not for a long time. She has to get used to them, to their smell and sounds. It's all new for her.

• Let them be in one room longer and longer next days. Step by step.

• To make her more calm you may give her catmint - it smells good for cats and calm them down.

• Don't let your cats sleep on her place. If you see, that she's angry or displeased, move your cats in another room.

• Feed her first. Always. And give them different plates.

• Don't let your cats play with her toys.

• Say your mother pet her more often, so she could feel her love and tenderness.

Slaps are OK, sometimes it's a part of a game or warning: don't come close. It's natural behaviour. But if they fight, the situation is more serious. As I can see from your post, your mother's cat just feels uncomfortable with other pets. It is understandable. Your cats are more friendly, coz they got used to live together.

Hope my advice will help.

I tried to bring them with me when I visited her, so that they can play with each other and all that stuff.

First things first: cats are not small dogs. You cannot expect them to behave like dogs; they're completely different animals. While dogs are social pack animals that enjoy "play dates" with other dogs and will typically get used to each other quickly (with some exceptions, as with any living creature), cats are much more solitary and territorial.

You may note that the number of cats walked on leashes in public is much lower than dogs; that there are no "cat parks" for them to play in; that there aren't outdoor "cat patios" at restaurants; there's not a lot of "cat boarding" options and no "kitty daycare" businesses. Cats set their territory, stay in it, and don't like invaders in it.

If you have a true reason for introducing them to each other, the answers for Recommendations for introducing adult cats to newly adopted adult cats and Recommendations for introducing kittens to adult cats may be of help, but you first need to stop thinking of them as dogs. They aren't "bowing down" or "approaching slowly to show no harm." They're stalking an opponent, who's outnumbered and anxious because there's suddenly two strangers in her territory.

But it would be nice if they would get along fine. That way we could give them to someone together when we want to go for holiday

This, too, is still dog-thinking. Just as cats don't like to have invaders in their territory, they don't like to leave it, either. The best option for a cat, when the owner goes on a trip, is to stay in their house with a caretaker either staying with them, or checking in periodically. The questions What information should we leave for a cat sitter/cattery?, First time cat sitting - what should I do?, and Pet sitting best practice are useful for understanding pet sitting in general, and cat sitting specifically.

Honestly, however, unless you're planning to move in with your mother, or your mother with you, stop trying to force your cats on each other. It's stressful to everyone involved, with no current benefit to anyone.