Some of this may depend on you and her aunt's financial situation and the type of insurance she has now. All states provide children with insurance if their parents/etc... earn under a certain amount per year. I do know that foster children are automatically given this, and that the program has a higher income limit than most govt programs (meaning you can earn more and still qualify than you can for other programs like SNAP).
While many people refer to this simply as Medicaid, each state usually has a different name for it. OH used to call it SCHIP, aka state children's insurance program but at one point they changed it. OK calls it Soonercare and it is great. It covers most things at 100% including dr visits, most generic medications and some brand name medications if no generic is available, hospital stays (both of J's week long hospital stays cost us zero dollars including the cost of meals from the dining service because a parent is required to stay with the child at all time), physical therapy, psychiatrists and tdocs, and much more. For several years they sent us a new nebulizer for Wiz' asthma every other year and when thank you needed to use one they sent us another for him every other year. All at no cost to us. The docs here recognize that it takes longer to get paid by the program, but they are very familiar with the guidelines and don't have to deal with the constantly changing lists from each ins co so they do not at all mind having patients with this insurance.
I would contact her current insurance provider, your local DHS office, and the state insurance board if you don't get answers you understand from the other 2 places. DHS can explain eligibility and if she is eligible how to get her covered and if theapplication should be made in your state or her aunts. You can usually get some answers online but may need to go speak to someone. We do the paperwork online here, but I don't know if all states do this.
Don't assume she cannot get the state kids insurance. Even though we can buy ins through husband's job, we still qualify for the kids' insurance through the state. It saves us a bundle and it makes life a lot easier for us. He gets paid well, but copays for the kids would eat us alive.