I'm replying to this, because I both agree with it, and disagree with it!
I was on the receiving end of something similar a few months ago, when my main band "discovered" I had a side project, and the BL was pissed off that I had a "secret". My "secret" was blown when we sent him an invite to the first gig - guess I need to work on my secret keeping. He gigs regularly as a solo artist (as do others in the band), but objected to my side project and asked me to cancel one of my side project gigs. When I pointed out he wouldn't cancel one of his solo gigs, he said that was different, because he'd committed to do those! In several years with the band this was the biggest conflict there'd been, but what I did in my spare time was none of his concern, and if I mark a night as busy in the calendar (as we all do), then that's a night I'm not available - no questions, because that's how it is for everyone in the band.
From that experience, the guitarist should be free to join another project, and manage her time.
Where I think this is slightly different is that she's playing catch up. She' s struggling to keep up with the band, and after a long break she needs to put some work in to get up to speed. The band did the right thing standing by her while she was unwell, but now she's back she should be repaying that with effort. If she can't do the work needed to learn material for one band, then taking on a second band is probably a deal breaker.
I think the band probably should have asked if she had the time to commit to both bands. It seems like she didn't, at which point she should have been allowed to make the choice. But it seems like there's a bit more history here that led them to make that decision for her.