When someone’s personality and behavior change markedly for no apparent reason, the first thing to do is to schedule a visit with her doctor. At 38, she is probably too young for a diagnosis of the onset of dementia — even though some of the behaviors you describe could indicate that. But there are a number of other medical reasons that can result in this kind of change.
Your dad should be taking the lead in this, not you. She is unlikely to listen to you since, in her eyes, you are just a kid. But your dad can probably persuade her that something isn’t right and that she should get checked out.
If all is well physically, your dad should talk to her about seeing a mental health counselor for an evaluation. The behavior with the dog and her efforts to be more like you are concerning. Sometimes this kind of behavior is a “regression”, a defense mechanism where the person retreats to a time when they felt safer. Often it is triggered by some fear or anxiety or stress that they feel is too hard to handle. The person then adopts behaviors that are typical of a person in an earlier stage of development. The treatment for that is psychotherapy to deal with whatever stressor is at the root of your mom’s distress.
I hope your dad and other adults in the family can get your mother to agree to an evaluation. It is unlikely that she will get back to “herself” on her own. She needs the support of professionals. You, your dad, and other people who love her need to better understand how to help her.
I wish you well.