I've never been divorced so I may not understand, but they really require you two to have your kid covered under two different health insurance policies? It may be the case, but sounds like a waste of resources. Which one is considered the primary policy? How do you coordinate benefits between the policies. I had fun with something similar when we worked for the same company and they required we each get our own insurance. We had fun as we had to pay double deductibles for the kids before they would cover them... until they sorted it in HR. I guess I could see the double insurance if your kid loosing her insurance through your ex would not be a qualifying event on your insurance for adding her. Again, another thing I don't know.
From what you said above, you could do a single HSA and fund it.