I'm sorry I didn't see this thread earlier......... but I am a dentist and I've treated this before. Disclaimer: I am not licensed in NY, just in Florida so below is just my thoughts, and you should check with her dentist.
I wouldn't stop the coumadin unless her doctor approves of the idea. I've never found any problem in taking Coumadin and Advil (generic name is Ibuprophen) at the same time as Advil really doesn't thin the blood much, if at all. But that's her physician's call. They may want to check her coumadin level.
Ask her physician if he/she could prescribe a mild pain reliever such as hydrocodone for immediate relief.
Brooksea is absolutely right, a lidocaine injection would instantly help. But if a dentist isn't immediately available to do that, then look into getting a night guard for her to wear. A night guard will allow her to rest with her jaw a slight bit open, which puts the TMJ (the joint area) into a comfortable rest position. If we're correct in assuming she has myofascial pain, then a night guard will help. She could wear it most of the day until she feels better. She can then cut back the amount of time she wears it until she finds a comfortable level.
And yes, muscle relaxers may help, but they won't work in the long term.
A dentist can make a mouth guard for her, but it will take time..... so how about seeing if she gets relief from a sports-type mouth guard? They're sold at Wal-mart for about $.99 and might help until a custom mouth guard can be fabricated. You'll need to trim it to fit her mouth. If that doesn't work to relieve the pain, then have her quit using the OTC night guard and see what her dentist says.
Hope this helps. I hope she's feeling better real soon.