Dear J.,
I'm sorry you are going through this. It gets very confusing.
I don't know about the laws in PA, but I'm pretty darn familiar with them in CA.
If you no longer qualify for health insurance through your employer because you are now a part time employee, your ex should have been able to add your child within 30 days. All you would have needed was something from the insurance carrier saying that there was a change in coverage due to no longer qualifying.
If it's been longer than that, I don't know what else you can really do. You can try calling the insurance carrier personally. Also, It's not automatic that open enrollments are in January. It depends on the anniversary date of the group policy. An aniversary date can be any month depending on when the policy was put in place. In that case, you have 30 days before and 30 days after to make changes.
It may be possible to get a court order through child support services where your husband has no choice but to add her, but I would caution you about doing this until you know for sure exactly what his group insurance covers.
It may not cover her asthma, allergy and ADHD medications. It may have a high calender year deductible that you have to pay before any benefits are available, it may only cover so many office visits per year. As far as orthodontia, those benefits are almost never covered in standard group health insurance policies and are separate, if offered at all.
In California, we have Healthy Families which is a program for working adults who make too much money for "medi-cal", but not enough to afford other coverage. You should see if there is an equivelant in PA.
Do that first because I know many moms in CA who's exes had to put their kids on employer insurance by court order, but the insurance offered was so crappy it didn't do any good and they lost their subsidised coverage on top of it.
I managed an insurance agency and I ran into this so many times and there was nothing I could do about it. In some cases, I could get an "individual" policy, for the child alone, but having $500 in expenses a month would be cost prohibitive for the insurance company to issue a policy that didn't cost at least that in premium every month.
Call your county public health department and ask them what programs they are aware of and what you may qualify for. It may be a blessing and something like that will work better for you.
I'm not trying to get Dad off the hook by any means, and I think it was great he was willing to work with you on this, but laws are pretty specific as to when dependents can and can't be added to an employee policy.
I wish you the best. Get info about other programs, make absolutely sure what dad's policy even covers in the first place and go from there.