Health Insurance Question/Dilemma

My wife had twins July 8th. The hospital said the twins would be covered under our wife’s insurance for their care at the hospital. Unfortunately we missed the 30 day marker to get them added under a life event. We never got told there was a timeline and found out once the bill came in for their 1 month appointment that they weren’t covered anymore and that it was too late to add them. Her employer didn’t know anything about that(he is the HR) but when trying to add them initially he said they were switching payroll AND insurance providers. When speaking with the new provider, they said to save the babies bills so they can be added on this new provider but its not until 10/1. So essentially our babies have no insurance until then? And even still, everything i read contradicts this saying their old bills can’t be covered retroactively. On top of that, our one baby just got admitted for a fever tonight.

Just trying to figure out if we are S.O.L. on these bills because it feels that way even though we are told otherwise. We live in Connecticut if that helps since states policies differ.