The gist of your story appears to be this:
Your husband doesn't like his job, and lied about having back pain in order to get some time off. He was able to get his doctor to disable him from work for three weeks, and his employer accommodated his leave under the FMLA. Right before the end of that three week leave ended, he decided to go to alcohol rehab. He contacted his employer and indicated that he was going into rehab. He didn't tell them that there would be a delay between when his approved period of disability ended and when he would be accepted into rehab. His employer expressed a willingness to accommodate his extended leave, apparently under the impression that his admission to rehab would be immediate.
Your husband was accepted into a rehab program a week later. His employer contacted him to ask that he submit his FMLA paperwork for the additional leave. You received the message and relayed it to him. He chose to ignore it until much later; perhaps even until he returned to work in mid-April. His employer noticed that there was a discrepancy in his documentation, with his being cleared for work during the week of March 23, and has asked that he document that he was disabled from work during that period -- as if he was not disabled from work, he should have been showing up and doing his job even if he was planning to later enter rehab.
Does that about sum it up?
Your husband has been advised to get a note from his doctor about his being medically disabled from work due to alcoholism, with his employers suggesting that they would find such a note to be adequate to bridge the gap between his two periods of disability, but (even though he has no problem lying to his employer about his back condition, or lying to his doctor to get out of work due to faked or exaggerated back symptoms) he believes it would be "unethical" to get such a note from his doctor. Except if he was in fact disabled during that period due to his addiction, and if a doctor was sufficiently familiar with his condition to render the opinion that he was disabled, there would be nothing unethical about the doctor's issuing such a letter.
Also, given that he applied for rehab and went through their intake and screening process, the rehab center should have an assessment of his condition in relation to the period of time at issue. But you say that he left the program after 14 days, supposedly due to a lack of insurance coverage. Looking at your dates, he went into rehab on March 27, left rehab on April 10, and returned to work on April 17 -- so is the actual problem with getting a letter from the rehab center that his employer might conclude was able to return to work as of April 13th?
I'm not sure how or why his re-entry into rehab would cancel out his CAM, although perhaps that's somehow built into the union contract. If the only way he can avoid facing the consequences of his prior actions is to find a way back into rehab, then that would appear to be the means available to him to keep his job. If he doesn't want to pay for rehab if his insurance won't cover another round, it sounds like it's time for him to start applying for new jobs. Given that he hates his job, that's not a bad idea anyway.

