Unless you have some legal document that forbids you to remove your children, travel between states in the US is not regulated. You are free to travel as you wish.
you dont
no
If both parents are incarcerated, the state's department of children's welfare will take the children into it's custody. If possible, the children may be placed with a relative before being placed in foster care.
For a vacation.
Yes.
Yes, it is possible
Fortunately, in most jurisdictions in the United States, a man cannot disinherit his wife and minor children. State laws provide that the surviving spouse can elect to take a share of the estate and that share varies from state to state. It can be taken in spite of a will that leaves the property to another person. It is possible to disinherit adult children but it must be done properly according to state laws in order to be effective.
Children go into a foster care home. These are homes that have been approved by the state to take care of children for long term care or temporary care.
Either take them with you, or let another family member watch them?
With permission of the other parent, or the courts.
Yes you can move to another state, but you can not take the children to another state till the divorce is given.
He can get himself to the family court as soon as possible and petition for visitations and/or joint custody of the children. Once he has established his paternity his right of access to the children must be addressed before the court will allow the children to be moved with the mother to another state. Of course, once established as the biological father he may become subject to a child support order as well. If possible he should seek advice from a family law attorney.