Assuming from your signature you are from New Mexico, there are 13 VA clinics sprinked around the state in addition to the VA hospital in Albuquerque. That is pretty good coverage - I can't imagine anyone being very far from one, and there is one in all the cities with population of any consequence.
As far as forcing doctors to accept tricare, medicare, or anything else, I'm a bit surprised to hear you say that as it is contrary to conservative philosophy. If doctors, hospitals, or clinics are receiving public funding then I would agree, however those that are private should have the right to run their businesses as they choose. Government interference is the primary argument against Obamacare. I would also point out that the availability of adequate medical care is, or should be, one of the considerations in choosing a place to live, just as schools, recreation, cost of living, weather, or any other consideration.
There have been several proposals discussed in Congress over the last few years to drop Tricare altogether and integrate it into the FEHB, which is what federal employees and retirees have, and which offers a choice of many different private insurance providers like Blue Cross/Blue Shield, which is what I have, so you can select a plan that has preferred providers in your area.
All this stuff continues to point out weaknesses in our health care system, which obviously needs its weaknesses addressed, but Obamacare is certainly not the answer, nor is socialized medicine like that in Canada, which has its own intrinsic weaknesses...
But, I agree 100% w you - private should mean private, and a doctor should have the right to decline anything they want to - so long as they went to a private med school and accept no form of government funded insurance. No argument there. The problem I see is - that isn't how the current system works...it hasn't for a long while. We almost never go to the doctor - but we pay taxes and premiums. Tax dollars go to support people that probably don't need to go to the doctor 20x a year, or shouldn't even be in this country. Under that set of rules...I really prefer my taxes go to tricare to the degree necessary to negotiate "reasonable charges" w doctors.
And, one of the things that really gets me about any medical care discussion in DC - it seems to be void of "medical schools", which almost all recieve federal money in one way or another. I noticed you said you have science degrees...I would be shocked if you did not know someone that was highly qualified, had all the right boxes checked, that applied and did not get accepted to med school. Why? Why not build more and accept as many qualified students as would like to attend? Vets command no where near the pay as people doctors, have a far more difficult and diverse 4 years of study...and it is more difficult to get into vet school than med school....but there is no shortage of people that want to be vets. So, the "no one will want to be a doctor if supply meets demand and prices drop" doesn't hold. Tort reform and tripling or quadrupling the number of student accepted to med school would solve a great deal of the the future med care crisis. It won't be done any more than they will eliminate entitlements to illegals.