Shorrt answer is yes, they can deny it despite the OB and Matria--just like when a patients' doctor says they need a heart transplant but their insurance won't cover it, or some other extreme example.
Long answer would be starting an appeal, but those can run for a long time and you'd need to know if you were to WIN an appeal, will Cigna then be required to cover it all retroactive to when they stopped paying (benefits at the employer is a great place for this info too). Otherwise even if you DID win an appeal, but it was after 6 weeks of fighting, you may still have 6 weeks worth of Matria bills to have to pay.
Drug assistance isn't for something like home health, and is only for those w/ both a low enough income AND no prescription insurance...and they also only cover actual prescription meds. Home health/pump/IV meds aren't billed under the pharmacy benefit but under the healthcare benefit. Also, since Zofran isn't officially approved for pregnancy/HG then Glaxo will not and really can't (liability) provide free. Sorry.
I like the idea of both asking Cigna (demanding?) for a new case manager, AND calling your employer. Often if an employer makes enough noise, the insurance carrier will bend on something...Cigna won't want to lose the business of that employer in the end and so are more likely to bend a bit. Another suggestion would be to call Cigna (not a direct line to the case manager, but the "general" line) and ask for whomever supervises all the case managers.