NEVER buy the excuse of a backlog!! Those poor folks you're talking to may not even be at the facility responsible for your ID card. They're embarrassed to tell you that they can't answer your question because they don't know the answer; so they use the "back log" story. Its been that way since the 70's when I had that job.
Please visit your closest VA Medical Center; NOT a VA clinic, a Medical Center. If you're not sure, call the Philly VA at 215 823 5800 to find out which is closest to you. You'll be asked to complete a form; they'll take a digital photo; you should have a card either right away or certainly no longer than a week. If you've done all this and its been more than a week, call the Patient Advocate at the VA Medical Center where you applied for the ID card.
About the braces you find restrictive ... call the clinic (Orthopedic or Prosthetic?) that prescribed them for their "open clinic" hours - you can go without an appointment but you might have to wait. Or, call to schedule an appointment. Braces are never natural feeling, but, they can be adjusted for more comfort.
You should adjust your expectations for depending on VA medical facilities while traveling. Generally, VA facilities in RV destination areas (Florida, California) provide care to larger veteran communities because they're popular retirement areas as well. If its a serious issue, you'll no doubt be next in line for care. If its a discretionary problem, you might be last in line behind vets with appointments. Adjust for that, and you'll be fine.
Pain meds such as hydrocodone; anxiety meds such as valium; and similar drugs are now under MUCH STRICTER controls. Generally, you'll not be able to get more than a 30 day supply and your provider has to authorize each refill. The providers are also now heavily scrutinized for excessive prescribing. Even in your local VA clinic or hospital, this class of medications is getting to be a real PITA. Imagine the hoops you'll have to go through from a different VA facility. Other meds such as insulin or blood pressure drugs should be an easier go if you unexpectedly run out while on the road.
Prepare a checklist before you go so you won't forget to take what you need. Aside from that, don't worry and travel around this great country that you served. Make sure you visit and support the VFW or American Legion or AmVets or any service organizations during your travels. Some might even have a place for you to park your RV.