OP--A couple of items to consider:
>>You do, indeed, have a liability issue, albeit a small one. If a child is injured while you are supervising the lessons, then you could have a problem. Again, small issue, but you should consider it nonetheless. (Note: Your homeowners policy--if you have one-- would not help you here, in part because you're accepting money for the lessons).
>>Perhaps, if there is no alternative to your group and the other group being on court concurrently, you could call the coach, in advance, and advise him of your plan. That might avoid the potential tension your wife is concerned about.
USPTA Prof 1/USTA 4.5