RMD will take families of kids not hospitalized. Our son may go into an eating disorder clinic on a day treatment basis and the clinic said we'd qualify for RMD across the street. Call and find out. This may help to put your mind at ease. RMD may also have lodging ideas for you if you don't happen to qualify.
I'm so sorry you're dealing with rude comments from people. The last thing you need right now when you're hanging on by a thread. Just know not everyone is judgmental and there are people out there who can help if you just ask.
I'd say a great game plan is to stay at RMD. If that's not an option, consider staying at a motel in a city outside of Palo Alto, like Mountain View, and driving in ... you'll get a better deal than a PA motel. Tap the local food bank for food if you're struggling financially. Palo Alto is a very expensive area, but you can find normal priced resources there. Avoid the specialty markets like Draegers and stick with Costco and Wal Mart if you want to get your own groceries.
For what it's worth, when I lived in that area, my boss had her baby at Stanford and had a positive delivery. The hospital has a great reputation.
Good luck with the insurance company. I'm currently fighting Kaiser to get the right treatment for our son. I know how frustrating it can be.
Best wishes on your upcoming arrival and I hope you can get a solid game plan in place for your time at Stanford.