Barring an emergency, is there any chance you could call your MW and go over what they are telling you and she could offer her input over whether any concerns they are bringing up are legitimate? If they are telling you it is an emergency and the baby needs to come out *right then,* then you will probably just have to put your faith in what they they are telling you and do what you have to do. In my opinion, some OBs might be in the "homebirth is unsafe and so I will do my best to discourage it" camp, but no one who is interested in keeping their license is going to suggest delivering a baby at 33wks for anything other than a legitimate medical concern. I'm not saying there aren't bad docs out there, heck there are bad MWs out there, but the chance that you end up with one who's anti-homebirth agenda is so strong they'd be willing to take a baby at 33wks just to make sure the baby is born in a hospital is pretty low.
If they find something that might be wrong that isn't an emergency, you don't have to make a decision *right then* about whether a c-section is really indicated or not and you'll have time to do some research and figure out whether you trust what they are telling you or not.
Here is a website that describes what the difference between a "reactive" (i.e. normal/ reassuring) NST is and what a "non-reactive" (non-reassuring) NST is. The ladder of testing usually goes NST, then if there is a concern BPP.
Here is a pretty thorough, albeit a bit technical, website on what they evaluate when they do a biophysical profile (a BPP includes an NST and the site has info on NSTs as well).
Here is a much shorter basic intro to the BPP and what they look for.
Personally, I'd consider just skipping to the BPP because, while the NST can help you feel reassured about whether the baby is doing okay or not, it doesn't provide you info like what position the baby is in, where your placenta is, and anything else that they could visualize that would help you know *why* you're experiencing decreased fetal movement. And the why might be important, if just to help keep you feeling more sane and reassured-- like if you find out that your placenta is anterior and the baby is posterior and therefore some of the sensation of movement is being blocked by the placenta, that would be reassuring to know. But then, I don't have any problem or concerns about USs.