If your children are in the presence of someone who you believe is a danger to them, it certainly should be addressed. Its unclear whether or not a judge would here evidence of an arrest record from 10 years ago, however if this person has a tendency towards violence you will certainly want that issue addressed in court.
As far as evidence goes, you do not necessarily have to have recordings for statements to be admissible in court. If your ex relayed this information to you, you can personally testify to what your ex told you.
It seems that you have ample evidence to prove the children may not be safe with your ex.

Erin E. Clarey
Attorney with Rosen Law Firm

Raleigh Office
4101 Lake Boone Trail, Suite 500
Raleigh, North Carolina 27607
919.787.6668 main phone
919.787.6361 main fax

Charlotte Office
301 McCullough Drive
Suite 510
Charlotte, NC 28262
Main Phone: (704)307.4600
Main Fax: (704) 943.0044

Sutton Station
5826 Fayetteville Rd. Suite 205
Durham, NC 27713
Phone: (919) 321-0780

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Found out today that my husbands ex’s new spouse (the kids stepdad) has a record of assult on a female. Unsure of any other charges at this time. He was drunk and beat the woman to the point of hospitalization. That was in 98 or 99. Well, now in 8/08, the ex told my husband that she tried to overdose and it didn’t work. Don’t have any of this recorded so it would be her word against his. She is now on several antidepressants or other mental health meds, unsure of what or why. Thinkning back out of the 4 kids( my husbands child and their 3), 3 of them have had soem sort of injury at one point or another. two have been burnt (one by motorcycle muffler and one by grabbing a curling iron) and the other stuck his foot in a boat motor last summer. Over Christmas, ex called wanting us to take the child to a new years eve party with them, they (ex and spouse) were so intoxicated, they couldn’t give directions. (the child didn’t go) with his conviction being close to 10 yrs ago and with light of everything else, would this be enough to bring to court for the safety of the child? Or would we need more solid evidence of neglect and/or abuse?