The damn-near trolling in this thread is getting ridiculous. He asked for actual help, not "screw cats" or "get a belt sander" or whatever.
The cat's old. If it had problems and lived in a house full of cats, it probably was never trained to actually go to the bathroom in "appropriate" spots.
It might also have urinary tract problems. Maybe. It almost certainly has social and mental issues.
Quite simply, this cat was never housebroken, and it sounds like the people in your house don't know very well how to housebreak a cat. Seriously, you
never take in a sick, old, or neglected animal unless you really, really know what you're doing. Your mom made an awful mistake. It's like taking in an abused child because it looks cute even though you've never had a kid in your life; you won't know how to handle it, and will get surprised when issues (obviously) come up.
You can't just rub a cat's nose in its mess; they aren't dogs. Punishment doesn't work well with them.
As far as litter goes, like I said, she probably came from some sort of awful cat-lady house or something like that, where she didn't have to worry where she urinates. Keep in mind that cats don't really have any way to know what you consider a "good" place to go to the bathroom.
Here's a thing I quickly googled on litter training:
http://www.perfectpaws.com/litter.htmlIt's obviously meant for younger cats, but it should provide some insight nonetheless. Not necessarily something to follow to the letter, but basically, you can't just assume that your cat will want to choose the litter box over anything else. You have to establish trust and good will with the cat and actively encourage her to use it. This is all made worse (much worse) by the fact that the cat probably didn't live a normal life, and is old.
In short, successfully training the cat will be difficult no matter what you do. This is a challenging situation, and I don't understand for the life of me how you or your mom didn't expect this to happen. You took in a possibly-ill, old cat, who obviously was going to have some problems; you guys knew this going in.
If she had to possibly compete for food previously in her life, you might face a couple problems there. She might end up overeating, or she might not. She might also get really nervous if no food is available. Just pay attention to her, really, and see what happens.