I would be cautious about this doctor. While it could all be legit, it does sound a little weird to me.
Do all these family members, including your wife, have clear Lyme symptoms?
I personally would not go along for this ride without lab testing to confirm what this doctor is telling you. That includes a Lyme Western blot. If it's CDC positive, you need no further testing. If it isn't CDC positive but there are positive bands (depending on which ones) along with symptoms, that would confirm.
I totally agree with WBF here.