What if divorce papers have been file with joint custody but the divorce is not final? Is a father allowed to go out of state for any kind of vacation or visit with consenting with the mother first?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

If the divorce is pending, then court permission to travel should be obtained. The mother should go to court to get an injunction against the travel

If the mother consents and it is anything outside the agreement you have already reached then make a document and have her sign it for the trip. There is no reason to not take a trip if both parents agree on it.

... Is a father allowed to go out of state for any kind of vacation or visit with consenting with the mother first?

He doesn't need her consent to travel.

If, however, there are children involved, and he wants to take them with him, that is another story.

Is there a custody agreement. Also a vacation is not like moving, if the one parent has visit or if the child is with that parent legally during that time, there is no reason he or she can not go for a vacation without permission of the other.

IT is moving out of state, or being out of state during the visit time of the other, that is the issue

Is there a custody agreement. Also a vacation is not like moving, if the one parent has visit or if the child is with that parent legally during that time, there is no reason he or she can not go for a vacation without permission of the other.

IT is moving out of state, or being out of state during the visit time of the other, that is the issue

Many states include orders that the other parent must be notified in advance when taking the child/ren out of state. Its not a big deal nor should it be.