Rocket:
First - good on ya for looking after Mom!
Second - try to use the term Care
giver - not Care
taker. I was making the same mistake - but kept catching myself and finally shook the bad habit.
Third - hopefully someone here will help you with the info you need but you could also reach out through their Nextdoor app for that area and see what shops come recommended by the folks living there.
I have a great mechanic here but it seems like every week someone in this area posts in Nextdoor "Who can you recommend to work on my car?" Followed by many replies and in those you'll see the same outfit repeated several times and that's when you know you have a good one.
I think your logic is acceptable on how to proceed with repairs but of course having a good shop looking at it would provide much better data for you to make your decisions.
Good luck and {{{{HUGS}}}} to Mom!!!
