My sibling

i have a sibling who has their own mental health issues who has also been having a hard time lately my mother wants them to have another assessment done by a psychiatrist only problem is the only psychiatrist avaliable in the whole city i live in is mine the next city with someone avalaible is 3 hours away. so naturally my mother asked if my sibling could see mine i said yes because what else was i meant to say but i am really actually uncomfortable with this. i cant even say why but i guess it is because i am so private about this stuff with my family and it is like they are intruding on my space hugely. how do i deal with this the appointment is made already.

also my psychiatrist has not said he will continue to see my sister but my mother is hoping he will and i really dont feel ok with that at all.