Is your fresh water plumbing still the original copper? If yes, can you fairly easily get to the pipes on both sides of the tub? If yes to that as well, I would be extremely tempted to replace the copper pipes under the tub with pex. Install fittings where you can fairly easily get to them, and patch in two pieces of pex, one for the hot water line and one for the cold water line. You might be able to use the old copper to pull the new pex under the tub.
If you have one split in the copper lines caused by freezing, you probably have other places in the lines that are now weakened by freezing. Might consider replacing all the copper water lines with pex. I know that would be a pain, but better than developing new leaks down the road.