I believe you'll have to go in and readd the characters to GoMule. Also, I would make sure you actually do a separate install. I think the registry will make all .d2s files go to the same "diablo II" folder.
Yeah it's going to be a big pain I think. If I were you, I'd put my original D2 + gomule on an external drive of some sort and then reinstall d2 for Path of Diablo. Then whenever you wanted to switch you'd have to swap them out. It might suck but your files gonna get all tangled otherwise. I've never installed path of diablo though, so I don't know for certain.
You gomule paths can be remade if you wanted to simply move your original d2 folder. They will be broken, but you can remove the characters/stashes in gomule and add them again in their new paths. I'm not sure about the saves. If you make new saves in your original d2 folder in its new path, they might be put in the wrong place (the path of diablo folder). That's why I suggest taking it completely off and having only one install, whichever you are planning on playing at the moment.