So my ex has been threatening me with custody of my two children. I have sole physical custody and he gets them everyother weekend. I am transferring for my job and he has stated the reasons he his wanting to take the kids from me:
He doesnt like my fiance (my fiance has a previous DUI arrest-however he was not charged with DUI, he has a CDV charge that was also dropped, he and his ex wife were both arrested on that)

my ex also also states that he wants custody because I am removing the children from school before the school year has ended (however Im transferring with work for a promotion)

he states that I do not have a car to get kids around and I do not but I will when I move due to my work relocation package

Also I have a worthless check charge from this year

We had a tax debt of 6000.00 that we did not address in our divorce and when he filed his taxes they took it from him however he was NOT suppose to claim our two daughters because they didnt live with him and he did anyways

Here are the facts I have on him:

He has not paid child support or kept up medical insurance

He has a VERY unstable work history and has moved to Raleigh with his gilfriend and her child into a two bedroom condo

He has been previously arrested for impersontating a police officer and spent 3 months in jail.

He has been phyically violent with me (while married) infront of my children. I have a letter where he stated this himself and also a letter my daughter wrote to me stating it too.

Also there were several times this year he took the kids out of school without permission for no reason and blantantly threatend my life and that of my fiance.

What type of case does he have?

In order to change custody your ex will need to prove that a substantial change in circumstances has occurred since the entry of the last order. Your move, if it is not far enough to interfere with his weekend visitation should not constitute a substantial change, nor should the presence of your fiancé in your life.
Your financial worries nor his are not necessarily relevant to any custody case.