About 18 months ago and after living in Europe and Caribbean I moved back to the USA and brought my mother along. For economical issues I couldn't apply for resident status and her entry permit has expired (about 1 year ago). She has a valid visa.

Now I am working in Asia and my family is innate USA. I am not sure we are moving here definitively yet but like to bring her over for a vacation.

We we are afraid that if she travel she may not be able to travel back to the USA, and we are not sure if we should apply for the residence before we move if we decide to do so...

I would like like to have her traveling in 3 weeks.

Please advise

What do you mean by "entry permit"? Do you mean the I-94? In other words, she has been out of status for 1 year? If so, if she left the US she would trigger a 10-year ban from coming back to the US. By the way, her visa is void because she overstayed.

You should help her do Adjustment of Status as soon as possible. She can apply for Advance Parole for free at the same time as applying for Adjustment of Status; she can get it in 3 months after applying. She should NOT leave the US until she either has the Advance Parole or has gotten her green card. She should not plan on traveling in 3 weeks.

I know this is of no help, but if your mother were Spanish there would be no problem.
For some reason if one is trying to do things the right way they make it harder or near impossible.