Since writing the above message, I have discussed the problem with my wife and found out that the problem isn't nearly so serious as the piano player led me to believe. Anne has decided, with no hard feelings, to sit out those tunes (or at least not play them on the accordion) where she can't play the chords the piano player wants. She also thinks that, with enough practice, she WILL be able to learn to play the chords the piano player wants. She just isn't that good yet.As it happens, the tunes my wife has been practicing on the accordian are tunes that were already in their repertoire. She came to last night's rehearsal prepared (she thought) to play accordion on 3 medleys out of about 20 in the whole night's set. (The tune list for the next gig had already been decided.) There was only one medley on which they couldn't agree on the chords, so Anne decided not to play on that one. It's no big deal, in her estimation.
I should point out that, although this particular problem is new, the band does have a history of having a lot of difficulty making decisions as a group. The band has nearly split up a couple of times over similar stuff. Hence the paranoia.
Maybe this a topic worth starting another thread about: How do bands make decisions? Appeal to authority? Phil Cunningham does it this way, so it must be right. Or, it's easier for you to relearn your part than for me to relearn mine, so let's do it my way.
Actually, the most convincing argument to me would be, "OK, let's do this tune your way and the next tune my way." But some people have a hard time compromising like this, and want to argue about every chord and every grace note until everybody else gives up.