Quote Originally Posted by julesy View Post
Is there any reason why I would not be able to replace the sub panel once I have corrected the back feed?
As JW has pointed out this service has several issues. I would recommend moving 'upgrading the electrical service' up near the top of the to do list. Particularly if you are planning on adding anything to it. Personally I would plan on ditching the tiny sub panel by adding a couple of junction boxes in place of the sub panel and pulling those circuits back to one nice new main panel. If you remove the breaker creating the back feed in the main panel you will open up two slots, one of which you can use for adding in the bathroom circuit.

Quote Originally Posted by julesy View Post
Can I run a separate ground from the main to the panel, or should I run a new 4 conductor wire? Once I have a grounded sub panel, I can then update the wiring that feeds from it, opening walls as necessary.
If you really want to go the sub panel route yes you can run a separate ground. Keep in mind that you cannot combine grounds and neutrals in a subpanel. There should be a separate ground bar in the subpanel for the ground wires. Most panels do not come with a separate ground bar installed, you have to purchase it separately and add it in.

Quote Originally Posted by julesy View Post
I see no reason why doing this puts the wiring in a worse situation than when I started - no ground to the panel and a back fed circuit.
When you touch something electrical, either to make repairs on add onto it, you are required to bring it up to code. Because your main panel is lacking both a main breaker and a separate ground bar (there needs to be one or the other) there is no way you can upgrade the sub panel and legally attach the ground wire to the main panel. (Connecting the ground from the subpanel to the neutral bar in your panel is a code violation.) Also you are adding load to a less than ideal setup and thereby increasing the risk that something will go wrong so in that respect it is worse.

Finding out what the problems are and correcting what you can is good, but realize the main panel has problems that are going to require that it be replaced and that it will be impossible to do any electrical expansions that will meet code until that is done.