My experience (and I might well be an expert on this one), is that seeking a relocation is a slippery slope with both the courts and the ex. I, like you, had 90% of the responsibility of child rearing.
I gave up an MSTP funded MD-PhD program because my child's father filed a restraining order preventing me from removing my son from the state after actually encouraging me to accept the out of state position. Had a huge custody battle that I eventually won. Fast forward 5 years (re-applied to med school and finishing the program) and match for residency in another city. My child's father waged another even more aggressive custody battle.
Are you trying to find a job on your own or are you using a recruiter? I personally love recruiters because if you have a good one they work their butts off to find the perfect job for you and it's no cost to you.
LECOM Class 2006
Osteopathic Family Practice Resdincy 2009
Locum Tenens: Urgent Care/Rural Medicine.