How do I stop an old dog from peeing in the house?

I am starting to take care of a grown dog who someone else raised. She is a 13 year old rat terrier and marks all over the house. I don’t know if it’s territorial thing, accidents (I definitely think she does it on purpose) or separation anxiety. She mostly does it while I am not home and occasionally during the night (funny enough she goes into the bathroom.) She has done it for years. Previously she lived with two other dogs and is far happier now they are not around.

I am hesitant to crate train her as I think it may do more harm than good and freak her out because she has always had free reign of the house.

I am moving into a new house and really do not want her peeing all over my stuff. Does anyone have any suggestions on how to stop this behavior?

Thanks for the advice!