Ammended Custody Per Sae

My husband had a child custody agreement that was part of his divorce decree when he lived in Dallas Texas. He moved to Austin with me and his ex-wife moved to CA. The original decree said that they had to say in adjoining counties. So I decided to do the amendments on my own. I sent in the Petition to Modify and got the case reopened. (I used my own custody agreement as the template to its all well written) and they sent in the order to modify (custody only) with the xwife's signature and it notarized. It went through the court process but was returned 5 months later because they wanted an updated signature of the xwife. By then she was claiming to take us to court for custody because she was refusing to pay child support so we were threatening not to send the kids to see her at Christmas (she also owed $5k in unpaid medical to me for the kids- original decree)
So I know in Texas a signed document is legally binding and it’s on record at the court it just didn’t get signed by the judge. I have three questions: 1. Will the new decree stand up in court?
2. If not will be at risk of losing the kids because he moved to Austin 1 month before she moved to CA?
3. If she wanted to get custody of the kids would she have any grounds since she agreed to be the non-custodial at the divorce, hasn’t paid child support until this year, and we have naked pictures and blogs about being drunk she has posted online? - Is this your question? Add additional information