My daughter has left her two kids with me and my husband many times in the past 4-5 yrs and takes off for days at a time. This last time we have had the kids sincer early May/2010. She then was evicted from her apartment and nowhere to go so we offered our home to her. She refused to stay there but left the kids with us and said she had to go be alone right now. She's floating from place to place, hotels, trashy friends houses, etc. At some point soon we want to protect the kids and get temporary/permanent custody. Is this the definition of Child Abandonment in the state of Texas?

There is a Sticky addressing the topic of abandonment which can be read here:
https://www.askmehelpdesk.com/family-law/child-abandonment-read-first-364259.html

If you feel that the children are in danger, contact Child Protective Services immediately. You'll need to give specific examples of what she is doing to endanger the children. Based upon the information you give them, they will decide if there is enough to warrant an investigation.

First off you should be going to court to get guardianship of the children.