custody btwn both sets of grandparents?

What is the name of your state? Arizona
Ok i will try and keep this as short and unconfusing as possible. My brother and his girlfriend have a 2 year old girl together. My brother is currently in prison has been for about 6 months and will be out in 2 months. His girlfriend has also been in and out of prison and is currently out waiting her trial. My parents the childs grandparents had called CPS on both my brother and his GF because of their drug use and selling also because of the neglect toward my niece (they would sleep in till noon or 1pm and leave the baby in her crib not changing her and crying. The last time both of them were arrested the baby was found in her crib with no diaper on and laying in her own mess. She had welts from being left in this condition. So my brothers gf signed temp custody papers to her parents so that CPS would get off there backs. She then moved in with her parents so basically it was just a way to act like someone else had custody of her child without it really happening. Her parents are somewhat better but still they are alcholics and the baby is always filthy. the GF's father has been arrested a few times for assault once that I know of against my brothers gf. Well now my brother is still in jail and his gf is so into drugs she doesnt care what is going on with her daughter her parents are raising her. My parents the other set of grandparents get my niece on tuedays at 5pm till morning and on fridays at 5pm till saturday at about 5pm. My parents have been doing this for about 6 months. They want to try and get custody of my niece. Can they win? The other grandparents only have temp custody so who would they be fighting. The other grandparents or the mom of the baby? We know that paternity has to be established as my brothers name is not on the birth certificate even though the baby has his last name but after that is done then what steps they need to take? Any advice would be helpful. Right now my parents are working at establishing that they have maintained a bond with her by having her two days a week. Please help! If you have any questions I will be happy to clarify as I know this sounds confusing. Thank you

Also, financially my parents are much better off than the other grandparents they own there own home in a very good neighborhood, they have NO criminal history unless you count a speeding ticket or two. They are elders in their church do not drink, smoke or do drugs. They would never raise a hand to a child and are the most loving people you would meet who adore all of there grandkids. They have more time to offer this child and are in there early 50's so they are healthy and able to raise another child