Can a doctor who is in my network refuse to accept my coverage because it is COBRA?
No. When you elect COBRA coverage, you are on the same group health plan you were on previously. When you visit a clinic, urgent care or an emergency card, you will present your health insurance card from the same plan you had while working. There would be no need to deny treatment because you are COBRA. All benefits you previously had, you will when you continue the employer-sponsored insurance.