Thank you for your clarification.
I see now.
As to jurisdiction for custody, this is going to have to take place in the state where the child has been residing for at least a period of six months. So if this was Florida before visiting in VA, Florida will be the state taking jurisdiction.
July will have to petition in Florida to take guardianship of her sister. Things would be eaiser if the mother would agree to this. But Florida does permit the filing for an "involuntary guardianship" when the parent of the minor is not able to take care of the child. This is clear given that the mother is refusing to take custody of the child. A relative who is capable of taking care of the minor can file. So July can proceed. Given that she lives in another state, she should have a Florida lawyer helping her with the paperwork.
You and July can review further information about guardianships of minors here
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