I was in a similar situation.
I opted to go back to school for my master's, and it looked like the new house we had bought was going to miss the closing window. This would allow us to walk away from the house, my wife could live with her family, and I would go back to school for 9 months. At the same time, we had been married for a few years and were ready for a family.
Literally 24 hours after putting down the tuition deposit, we were informed our house would close on the last day possible for the builder. And a week after we stopped using contraceptives, my wife was pregnant. So I was living ~90 miles away from my pregnant wife, she was the sole bread winner, and her due date was 2-3 weeks after my scheduled graduation.
Things were nuts; I lost 30 lbs in 6-8 weeks, and weighed less than I did when I graduated from high school a decade earlier. Major financial stress, panic about the pregnancy happening so quickly (we were expecting a year of trying due to health complications). Also the RAPID adjustment from full-time student to dad to working full-time (I acted 5-10 years in those three weeks).
My advise is to try and make things as comfortable for your wife as possible. Surprise her with her favorite snacks, Take your daughter out to the park so she can sleep in. The less stress she is under, the more she will relax (if you're anything like me, her stress becomes your stress).
I would also HIGHLY recommend talk therapy. I found this was a major outlet in terms of venting about the stress I was under, as well as helping to sort out my thoughts and emotions in a way that will help you from feeling overwhelmed and helpless. And if you're still having trouble, a professional can also point you in the right direction for any medication that you might need to reduce anxiety and stress so that you can focus your energy on your family.
I definitely feel you on the sleep front; I couldn't fall asleep, I was CONSTANTLY freaking out about all the stuff on my plate. And I didn't have another child at the time (I have two now).
The fact that you are so focused on everything shows you are a hands-on dad and husband, which is awesome. Try not to feel overwhelmed; I would also recommend a stress buster. I played dodgeball and indoor soccer. That one night a week got me out of the house, meeting new people, and working off a lot of my negative energy.
I have no opinion on whether or not you should go back to your old house; it sounds like a LOT of change happening at the same time, which is why the old house is so appealing: one thing remaining constant. Do what is best for you and your family; but consider that you can make the new house a home for your new family (four is VERY different from three).
Good luck, and try to keep a positive mindset. Also, lean on your in-laws. Get some free babysitting to go see a movie before baby #2 arrives!