I say be very, very careful. If your body doesn't tolerate the abx very well, and the rash progresses - stop all abx - no matter what any practitioner tells you. It can be the start of a serious allergic reaction.
Otherwise, rashes showing up anywhere on the body during treatment for Lyme isn't all that unusual.
I'm like you, Girlie - I just don't trust the doctors any more - I've had too many - uhm, shall we say, disappointments? Fairly major "disappointments", although they didn't turn out like your situation with your Dad (so sorry to hear this!!), fortunately.
It's been my experience that very, very few doctors like their patients knowing much - and like it even less if their patients' spouses know more about
a subject than they do!!
Although there are a few doctors out there that do appreciate a well-informed patient - the doc I'm seeing now is really wonderful. We actually discussed my having gotten reinfected, testing options (I opted for none) and my treatment!! She wanted me to go for IV abx and I wanted to try my herbal treatment again!! So try to talk with them intelligently, but be prepared for your doc to not like it - just in case.