Am I out of line to ask a relative not to go to the doctors with my mom and I?

It is definitely better to keep the lines of communication with the other relative open AND to approach it as a "we all have MIL's best interest at heart and we appreciate your willingness to help and to stay in touch." I was POA for my uncle and guardian for my aunt who is in a nursing home. It began with my uncle's kids trying to handle things, and when I was apprised of the problems, they were very thankful to have me be involved and helping. I always approached it as a "we" effort, and we had a "family" group text to keep everyone aware. When one of us would get upset about something, the others would be a calming influence, and we always reminded each other of the goal of doing what was best for my aunt and uncle (their dad and his wife, my mother's sister). We each had our strengths - one was very good at keeping records, the other was very good at being aware of my aunt's needs, and seeing that they were met, and I was the general overseer, dealing with the legal and financial issues and making the final decisions if we could not agree. I was able to be the calming influence with my uncle, who would take rage at his children for being incapacitated himself and unable to care for his wife. When he passed away, his children handled his funeral arrangements and clearing out the rented house. I found an attorney to handle the estate, asked the legal questions we needed answered, and helped advise them. I may have been able to do it alone, but believe me, having them made everything so much easier - even when we disagreed and people were losing their cool. Because even the disagreements were helpful in looking at things from different perspectives - God knows I didn't have all the answers, and don't always know what the right thing to do is. And more than once I had to remind them that their dad's body was not sound, but so long as he was of sound mind, he got to make the decisions and our job was to implement them, not to make his decisions for him. So I would advise welcoming the help, while being firm that you need to be in the loop and that you would love their input and collaboration as one more set of eyes and ears on your MIL. When you are overwhelmed, you will be grateful that you have someone already familiar with what's going on to call on for help, so long as they are cooperative.

Asking the relative to work with you in the future as suggested by Eddie is a great idea. Be positive and express your appreciation. While you are having that discussion perhaps bring up some other aspects in which the relative can help...calling her dailty to check in on her and txt you afterwards to indicate she is ok....or shopping for her once a month, taking her to coffee or lunch weekly or monthly...assisting with laundry, or cleaning the refrig. ANYTHING that helps your mother and relieves some stress off you and your husband.
You may find you can cultivate the relationship with the realitive to behefit all. They may welcome an opportunity to help out as they can. .... or the realitive may run for the hills.

LYNN:

As caregivers, it's comforting to know there's an extra source of strength somewhere. While deep inside you appreciate this relative's concern and willingness to help, no one likes an interloper. Particularly when you can't figure out his/her intentions.

Whether you're out of line or not will hinge on how you present the issue to this individual. I'd say something like "You have no idea how much I appreciate what you're trying to do for Mom. It's obvious WE want the best for her. But the next time we need to coordinate our efforts a little bit better so we can both be on and read from the same page at the same time." Then end the conversation with a hearty hug and a big "Thank you SOOO much!"

Boz, thank you for the reply. My husband and I will be at the Dr appt. Mom, is a little competent. We believe that she has some demenita, but she is the one that can choose which Dr to see and if she would like to have the relative with her at the Dr. appt. But the other question is, would be out of line to make a request to the relative that in the future, if they are made aware of a health issued to please contact us right away and not just go ahead and make Dr appt?

It was to be frustrating to be doing so much for so long and then have someone else jump into the middle of things.
Is your mom competent? If so she can agree to see any doctor she wants and attend with anyone she wants. After all you've done that is probably difficult to stomach. IF it were me I'd try to attend the appt with your mother and the other family member.
If you cant' make the meeting perhaps you can get mom to sign a form the doctor will have in the office that allows you and your husband to call and ask questions or secure a copy of the record.