Re: taking custody of children in family
Here in AZ, if the kids are placed in foster care they go to a licensed foster family first then CPS looks for any family to step up. If they find family they would place with the family as a kinship placement and the kids would only be in a foster home for maybe a week. They would do a quicker homestudy and then give you time to take classes. You would not get the payment for caring for them until classes were completed.
Here, I believe, you could also petition for the child that is already in care as CPS wants to keep families together if at all possible. I know we don't have a child limit but I think in CA (which has a 6 child limit) they would make exception for kinship placement.
It wouldn't hurt to call and find out about the child already in the system to see if you could get custody to keep the family together.
About the living conditions, I would be calling everytime I knew something was going on- daily if need be. Call anonymously and report the diaper changes, or lack of, the feces on the floor, the asthma issues, the dust mite allergy. Does the 5 year old attend school? Talk to her teacher and make sure she is reporting if she is seeing any thing.
Hope you can get these children out of this sad situation.