How does my daughters dad get permission to be around his daughter when he is a sex offender

He needs to start with his probation officer. Whether permission will be granted depends on the nature of his offense and the offender level assigned to his case.

Your other question pertains to how "he" finds out what level offender "he" is. "He" asks his Probation Officer. It is also in his Court papers and often available on line.

Thanks so much. And ware would I go online to find it

The local sex offender registry will have his level

Unless his sex offense was against small children or his own daughter, he may not need any special permission to be around his own children. But he can discuss this with his PO assuming he has one.

Next he gets to be around them by having court ordered visitation ( also assuming you two are separated and not living together)

People are sex offenders for urinating in public or for having oral sex at 18 with a 16 year old girlfriend, so the term sex offender has little meaning unless we know the actual crime and level of sex offense.