That is tough. A cat allergy is a bid harder to manage than others because, as my doctor explained it to me, cat dander gets every where and is sticky. If you don't have a cat and your neighbor does and it happens to come into your home once a month...it is just like you having an indoor cat because the dander is there.
So, while bathing the cat and cleaning regularly helps it certainly does not remove the allergens completely. Did your Mom know daughter was allergic when she got the cat even though she knew your daughter was there often? If so, that is a shame. Can your mom watch your daughter at your home instead? BTW...your mom could carry some dander to your home too?
My daughter takes Zyrtec in the am and Singulair in the pm. She also has to use a nasal spray and/or eye drops when her something triggers her...plants, pets, and cigarette smoke are the worst. She was briefly exposed to some cigarette smoke at our neice's birthday party and has been coughing since...breathing treatments for over two weeks now and we had to get an antibotic and steriod last week. She's on the mend now.