How to do your own prenatal care?
I don't know the answer to the insurance question. But I'm not sure you can find an OB that would only let you come in when you wanted to, for tests and such that you determine are important. That's just not how they operate. A midwife may be more open to the suggestion, but also may not be. Depends on the Midwife.
As far as UPing (Unassisted pregnancy), you can do most care for yourself such as keep a food diary to keep your nutrition in check. Check your own blood pressure at the grocery store. Keep your weight gain in check. Know what indications mean something may be out of balance..like swelling (not enough salt? Too much time on feet? etc). Or headaches and seeing spots etc.
If you want blood work and tests that's kind of hard to do on your own. There are lots of sonogram places around these days, but they are not usually diagnostic, they are for looking and getting pictures. Some will do gender identification and that's it.
The reality is, this depends all on your comfort level with pregnancy and knowing your own body.
Your insurance should cover any bloodwork or care that you need. Mine did. I did not go to an OB for tests, I went to a clinic. It's easy to just go in and say "I'm having a home birth with a midwife (yes, I know, I totally lied) and she can't order bloodwork for me." They ran tests for iron levels as well as a lead test I requested just to be on the safe side. They didn't ask questions and were happy to do it.
You won't be able to get ultrasound without going to an OB, however. I personally am against ultrasound unless I strongly suspect a problem, but that's up to how each individual mom feels. I believe they are unsafe and would rather not expose my baby unless I feel I have to.
I did my own prenatal care the second time around after seeing how easy it was with my midwife the first time.
-check blood pressure at grocery store or get a blood pressure cuff to use at home (they make automatic ones now as well)
-urinalysis strips are easy to obtain and inexpensive and have directions right on the box. This is the brand my midwife used: http://www.amazon.com/Response-Parameter-Urinalysis-Reagent-Strips/dp/B001EUAXZM/ref=sr_1_1?ie=UTF8&qid=1338705723&sr=8-1
-check weight on bathroom scale
-watch for signs of problems as IntuitiveJamie said above
-take own temperature
-check iron and heavy metal toxicity levels at local clinic
-check blood sugar levels with a blood glucose monitor (I didn't do this with either pregnancy)
-purchase a fetoscope to monitor baby (doppler is ultrasound, so a no-no for me)
I made a chart in Word and printed it out to write my info on throughout my pregnancy. I kept it in a folder with my other medical info to take with me in case I had to transfer to the hospital for any reason.
We decided to forgo any ultrasound for our last pregnancy which we did UP and UC. That was mainly because I would have had to see the doctor to go over the ultrasound and I really didn't want to do that. When I was still considering an ultrasound, I managed to find a place that does them for free (one of those Christian Pregnancy Crisis centers, which will do them whether the pregnancy was intended or not) but their cutoff was 24 weeks and I was at 26. If you're eager to do one, but don't want the hassle of doctors/appts, I would recommend that route. Of course, not knowing the gender ahead of time is fun because it tends to drive the people around you a little bit crazy :)
That's what I do. And also, someone said that an OB or whatever might not let you forego some appointments/tests. That's not true. I skipped appointments with my twins and also with my last baby (they get annoyed, but they can't do anything about it), and they have no problem if you don't want to get weighed, pee in a cup, get a cervical check, etc. You can always decline those things, and you can decline the GTT and ultrasounds, too. However, I usually do those things anyway, because I feel it doesn't hurt to get those tests done, and I'm okay with 2 ultrasounds, an early one for dating and then the anatomy scan.
I tried to skip appointments but it didn't work at all. When I tried to schedule my next appointment, the nurse said, oh, you can't have that one yet, you havn't done your XYZ appointment. Also, you can refuse anything but they might get grumpier over time about that one. It might work better if I had more kids and could use them as my excuse, or if I had the courage to tell them, "look, I don't think these are helping me at all, so I'm coming to only half. Make them count." and stuck to that. Probably will never bother doing that, my current midwife is the best, so I've just gone t o everything. Oh darn that reminds me I forgot to schedule my next one! Ah, this is what I mean, there's so many things to go and do its just hard to remember period, you'd think they would understand.