You don't explain whether the father is your husband or not. If this is a situation where you are not married and there has been no order of paternity entered establishing him as the father, you technically already have full custody.
If you are married, you would need to file a divorce or legal separation in order to have the court award you full custody.
Whether the children would be placed with their father or other family if you are no longer around, would be up to the court and the situation at the time. If the father is deemed not fit to have custody, the children would likely be placed with other relatives until the father is able to become fit or has his parental rights terminated.
You should hire yourself an attorney right away to review your situation and retain your full custody and child support rights. Good luck!
This should not be considered legal advice, but rather simple information. You should consult a lawyer to review your unique situation. No client-lawyer relationship exists until you sign something indicating there is.
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