If a have a burglary and fraud charges from 4 years ago, would the judge not let my girlfriend get joint custody because of my past?

I caught a burglary and theft charges 4 years ago. It was the only time I've been in trouble. My girlfriend’s ex-husband has temporary custody of her girls, and she is going soon to get a visitation modification. Will the judge look at it as a bad idea to grant her the change with my past? She's unsure on whether to give me the boot in regards to her children which she doesn't want to do. So I'm just wondering if they could use that against her and if they would even do a background check on me. I messed up once, and have turned my life around, her girls love me and I love them. Can someone please give me advice?