COBRA being indirectly avoided

I was laid off due to lack of work at the end of April. I was notified of cobra coverage, which I elected. It was done through a 3rd party, and I have sent in two payments so far. I paid my first premium at the end of May, and they sent the first email on May 28th.

I've been bouncing back and forth between my insurance company and the 3rd party that handles taking the payments, etc. The third party has not been authorized by the 3rd party to directly contact the actual insurance provider, and must be authorized by the employer before it can.

I have gone nearly a month and a half without medications (such as antidepressants, diabetic supplies, and allergy medications) because coverage ended April 30th. It is now almost June 30th, and while I have paid, and been paid in full, for nearly a month - I am unable to get coverage because they are waiting on my employer.

Other than the incredible amount of stress, anxiety and generally feeling ill due to not having my meds, my wife is pregnant, and we are trying to see our physicians and are now starting to get bills because coverage is being delayed.

I'm not ready to pursue legal means quite yet, I just found out they are the roadblock today. However, should they continue to give me the runaround I want to know my options so that I can pressure them should they try and pull something. Should they be unmoving, I would then be willing to have a consultation to figure out what my legal options with a lawyer are.