I would definitely find out what the hospital has to say about labouring/birthing in their tub. I laboured at the hospital with my first in their regular tub, with just the shower head on me. (They wouldn't let me have an actual bath b/c of the old fear of water getting in, infection etc.) But that was still helpful.
And yes, it will be quite busy having a baby and a little one at home, but I personally found I was so much happier that it was better that way. I was getting SO SICK OF BEING PREGNANT!!! I could hardly roll over or get out of bed. Getting up to check the kids or go pee at night was brutal. I could barely walk when I stood up. I was so sore and tired and emotionally at the end of my rope. I started having false labour and that was also very stressful - I thought I must be truly going to have this baby, and then the contractions would die out. I had two stretch and sweeps done, and a combination of herbal extracts prescribed by my midwife to encourage labour to start. Your feelings about pregnancy at this point are perfectly normal! It is a pretty miserable time for a lot of women, and it sounds like you have a particularly rough time. But give yourself a little more credit - you CAN do it! Hang in there! Oh, and can you see a chiropractor for the neck/back trouble? Lower back pain during pregnancy is pretty common, but the a chiropractor would likely be able to correct the neck issue, and possibly even help the heart-burn. And having your back and hips properly aligned before labour will give you a better positioned baby and an easier delivery.
All the best!