Legally, for my MW to attend at home, I have to be 36 weeks. But, her rule is 37 weeks (although I'm sure there is a little wiggle room there). I'm 36 + 3 today, and in the unlikely event of labor starting before 37 weeks, I'd probably choose to stay home by myself unless I felt something weird was going on.
Minimum estimated gestation before being admitted - Page 2
34 weeks for a HB? OMG! That is a horrifying thought. I know someone who gave birth at 34 weeks to a baby who breathed perfectly (was planning a HB but gave birth at the hospital given the gestation) but that was seriously lucky. Many babies can't breathe well on their own at that point. My MW is willing to attend at 36 but did say there would need to be a thorough discussion of the potential risks if we find ourselves in that situation. 37 is far more preferable. Both kids have been born right at 38 weeks so I'm curious when this one will make it's appearance.