You will first and foremost need to articulate why sole custody is in the children's best interest. You have a good basis 1) Housing and sleeping arrangement although you note courts will find any room acceptable, and the multiple children in one room is also acceptable. You will need to show that there is not enough rooms in the home.
2) School, this is a fundamental requirement that children get educated and get to school on time. If you can show the children are being short changed by being tardy, grades are below average, this may make an impact on the judge.
3) failure to adhere to visitation schedules is also a key point. courts want children to have access to both parents. the fact you have needed the police, and potentially court assistance in enforcing the court order also is in your favor.
4) It may be worthwhile to get a Guardian ad Litem(GAL) to represent the children. The court will listen to the GAL's recommendation which should include what the children want to have happen.
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