Mom's dog wasn't trained properly or socialized with other animals. I'm afraid it will bite her. What can we do?

Several months ago we moved my MIL into a house we own right next door to us. She has early to mid ahlzheimers and we wanted to be able to be closer and make sure she eats well, takes her meds etc. We have taken over control of her finances because she was being scammed and loaning money to people she shouldn't. She wanted her car, so we brought it to keep her happy, but made sure it will not run. Adjustment was a bit rough, but is much better now. Our next hurdle, is she has a little Yorkie that she loves, but the dog has bitten her a few times. 3 times to the point of drawing blood. I don't think it is safe that she keeps the dog, but when we have brought it up she gets heart broken and always says "it is the 1st time she has bitten me:. I went over this morning and the dog had bitten her finger and drew blood. My mother in law has lost so many things...her home she lived in for years..her ability to drive, her independence, managing her money, that it breaks my heart to take her dog away also. But for her safety I know its what needs done. Keeping the dog at our house is not an option. We have 2 dogs and 3 cats already. Her dog was not trained properly or socialized with other animals. This might be the hardest thing of all because she always talks about what good company the dog is, and she doesn't know what she would do if she doesn't have her. Any ideas how to handle this? When we are there the dog knows it has to abide by the rules and not bite, but we both work so can't be there all the time. It usually happens when my mother in law does something that makes the dog mad, like take something from it, or try to put it outside. The dog definately thinks it is the alpha when it is just them in the house. Today I told her it scares me that the dog might bite her so bad she needs stiches someday. Sorry this is rambling but I am upset!