Some times it falls on me to provide information that may not be the most favorable to the customer, but do note I have a professional obligation to provide you the most accurate answer I can so you know your rights and can act on them.
Are you online with me? If so feel free to reply here and we can go back and forth with a conversation until your question is answered.
If I correctly understand the facts your ex-girlfriend is the only party on the deed to your home due to your back child support and the potential of a child support lien. Please correct me if that is wrong.
That being the case yes she could go through the typical eviction process. She would need to provide you 3 days notice to vacate and could then start the eviction filing. Then a constable would serve you with the notice of a hearing on the eviction no sooner than 5 days after you are served. At the eviction proceeding she is only required to prove that her right to title is superior to yours. There is the ability to appeal so it can be delayed for a period of time, but to answer your question she can do that or if she deeds it back to previous owner he can also use the eviction process.
Have you considered filing for divorce and claiming that you had an informal marriage (common law marriage). You would need to show the following
An informal or common-law marriage exists in Texas if the parties (1) agreed to be married, (2) lived together in Texas as husband and wife after the agreement, and (3) there presented to others that they were married. See Tex. Fam. Code Ann. § 2.401(a)(2) (West 2006). You would definitely be entitled to an equitable portion of the homes value no matters who's name is ***** ***** deed.
Let me know your thoughts and any follow up questions you have for me.