That boyfriend needs to go bye bye. You have done what you need to do for your Mom and be grateful that you have doctor's that will support you in doing what needs to be done to keep your Mom safe.
In this situation, I do believe that what the doctor's are doing is correct. With an outsider (boyfriend) trying to gain control of her finances, the competency evaluation is much more important. The Dementia diagnosis will give you an explanation as to which Dementia is causing the incompetency but for now, the fact that she is incompetent is most important. If she is not competent then she can not change the legal papers that gave you and your brother control.
I am not sure where you are but here it is a legal decision as to her competency. If you have two doctor's that are declaring her incompetent that is overwhelming evidence but you can never be 100% sure what a court will do. Can I assume that this boyfriend does not have the financial well being that your Mom has? Make sure you have a good lawyer, familiar with competency cases, on your side... and be sure that information regarding this boyfriend is available to be included in the evidence since he is helping her. You need to know his motivations. You will also need examples of irrational behavior by your Mom. This supports the doctor's claims. Don't try to do this yourself.
Remember that Dementia (of any kind) is not just memory loss. It is also changes in behavior, the inability to think logically and rationally, the inability to use good judgement and make good decisions. Those with Dementia may believe that their decisions are sound and rational. They may believe that they are fine and that it is you that is being irrational. Because this is their reality and they believe it just as strongly as you believe your reality, they may seem very convincing. That is why you need all the evidence possible when it goes to trial and the guidance of a good competency lawyer.
Instead of tearing the family apart this should bring the family closer. What you are doing is right for Mom and what she needs. It is protecting her from herself and her boyfriend. You need to keep your focus on what Mom NEEDS! What she wants, and what the boyfriend wants, are not your objective or responsibility. Your responsibility, now that Mom can not make such decisions rationally, is what Mom needs.
Has the doctor told your Mom not to drive? If not he needs to do that immediately and notify the proper authorities. They will take away her driving permit. If the boyfriend insist that Mom drive to him without a permit then that is an irrational act by both of them. I would definitely tell the boyfriend that Mom is required to stay with the care givers per orders of the doctor and that is how it will be. If he can not abide by the instructions of the doctor, then that is also an irrational act. So just keep doing exactly what you are doing and I do hope it will all turn out well. My bet is, when the boyfriend fails to gain control of the money he will disappear