My first thought was to notch out the frame to the height of the tub, then patch it up after the tub is in place, but it now seems like the patching would take a tools and a level of carpentry skill well beyond me. Next, I thought about removing just the offending side of the frame, reinstalling it later, but the way the frame seems to be joined together at the top makes this impossible with the frame in place. So, it looks like the entire frame has to come out, to be replaced with a new one or possible reinstalling the old one if I don't damage it too much.
So, the question is, how difficult is this job? My carpentry skills are only modest. I've seen that HO will install a new frame for $150 labor, so it can't be too bad.