Well I know Momiji is a bad MU against Hayate, Idk how the MU between Ayane and Kasumi is, but I lost to his Ayane so I guess Kasumi is a bad MU between her, and Rig....Idk what to say about that
Momiji can fight Hayate fine. Her neutral game is much better than his. Kasumi only struggles against Ayane at range. In close Kasumi is the one in control especially when she's on the advantage. I don't know Rig much except that he's vulnerable to hi-crushes and sidesteps when trying to pressure with his flamingo stance. It's a case of understanding his frames and picking your spots wisely.
Just find any matches of me using Kasumi and Momiji in the archives. If there are some matches that are paused for a long duration, you can ignore em. Same goes for any matches that are somehow skipping, bugged, etc. Don't know why that happens, but it happens.
When fighting Ayane as Kasumi, you pretty much have no reason to back away from her (I.e. You don't need to use 7P). Your goal should be to stay on Ayane's ass as much as possible and not give her any room to breathe. When you get a KND, do not back away, instead oki pressure her on the ground with 2K, 1P, 4H+K, or 9K. You can use 9P+K flips or 9P to change positions (though take note of their retaliation).
The most recurring thing I noticed was getting CH by 4K or 6K. If Ayane is trying to nail you with 4K, simply block and punish it. If 4K is whiff punishing you, be careful with overextending your pokes, i.e. poke with moves with fast recovery or space your pokes better to avoid punishment. It is a tough move to SE the follow-ups.
If Ayane is running at you can protect yourself with your parries like 3H to OS her mid strikes. If you're at neutral, you can CH her with 6P/6PK/6P2K, 4P/4P2K, PP~strings, 3K/3KK, or if you're feeling ballsy, even 7K. Generally your safest option is to just block, until she starts trying to throw you, then you can CH launch with 33P or 236P.
During approach against Ayane, Kasumi is almost always at the disadvantage due to how potent Ayane's keepout is. You made a nice get-in with 3P+K, but you also got nailed by 4K another time. On approach you can try run-up 3K, 66P or 66K. If you detect a backdash, 66H+K is a good stepkiller. Getting in won't be easy but when you do get in, be sure to stay in!
Overall I'd say that your cousin reads you better than you read him. He also seems to catch you with random pokes at times, which don't always make sense. If you block a poke that leaves Ayane FT, PP~, 6P~ or 2P as retaliation. For BT, be careful of BT8P whiff baits.
As a rule of thumb for approach, the person doing the "approaching" is usually the one at disadvantage unless they have ranged moves that can outrange the opponent's "keepout" moves.