There is so much misinformation in this thread that I am scared to continue posting in it.
First of all, ultrasounds through Tricare Prime are not confirmed/billed through the PCM. If an OB is "writing off" ultrasounds, he is an idiot. All he has to do is code the ultrasounds properly and Tricare will pay for them.
When a patient gets pregnant on Tricare Prime they usually get care through an MTF. If that isn't possible, they are referred out into town to a civilian OB who takes Tricare Prime. That civilian OB does not have to answer to a military PCM when deciding their standard of care. That is literally backwards as a non OB PCM has no expertise in deciding who should get an u/s. I had dozens of ultrasounds during my pregnancies and never had a single issue with Tricare nor did any person other than my OB have to approve them.
OP, you are literally 5 weeks pregnant. Wait until you have met with YOUR DOCTOR (not some nurse taking blood) before you start researching private ultrasound places. If you need an ultrasound and you have a good OB, you will get an ultrasound. Tricare has nothing to do with it. Tricare will cover whatever is medically necessary. If you feel like you are getting substandard care, then go to a patient advocate and get switched. But I would seriously wait until you have met with your actual OB before worrying about them dating your pregnancy by feeling your uterus. Yes, they do palpate the uterus to guesstimate things. And yes, some OBs only do one ultrasound between 17 and 20 weeks.
I would bet a whole lot that you are misunderstanding a bunch of things and being newly pregnant you are a little worked up. Just let the next few weeks go by, go to your first appointment, ask a zillion questions, and if you still are confused/unhappy then work toward getting a different OB.