We ended up keeping the tub, and I spent an afternoon scrubbing all the stains with Lime Out. Seriously, I scrubbed until my hands were raw, but it worked. And it now looks new. I'm so glad we decided to keep it because that tub style is very hard to find. And I'm glad that we didn't have to re glaze the tub. After doing some research we found out that it's not so great with children and everyday use.
Since we had to re-pipe the whole bathroom, I had them take out the large radiator and move the sink to that opposite wall. Good decision because we acquired more vanity space. We put a toe-kick heater in place of the radiator, which is located under the vanity.
I bought many of the fixtures from Vintage Tub--great online resource if you want the vintage bathroom look or need to replace vintage bathroom pieces. Prices are good. Below is a list of other resources and before pictures.
Honeycomb Italian Carrara tile (flooring) and subway tiles (shower)--Lima Ceramic Tiles (local)
New window and toilet--Home Depot
Tub faucet/rain shower head/sink faucet/shower curtain rod--Vintage Tub
Sink Vanity and countertop--Restoration Hardware
Medicine Cabinet/towel rod/glass shelf--Restoration Hardware Outlet
Toilet roll holder/single towel ring--Restoration Hardware
Lighting sconces--Lighting Universe
Paint color--Benjamin Moore White N33301 (beadboard and ceiling) and Quiet Moments