What to do if my ex-husband wants to fight for custody of our 4 kids?

Texas uses a standard of "best interest of the child" when deciding who should be awarded custody.  If he has a history of domestic violence and you can demonstrate that history to the court, then the court can deny his request for sole managing custody.  The court would then need to decide what type of visitation rights-- if any-- he should be granted.  If his violence is only directed at you, then they courts may allow visitation, but order that it be supervised by you or a third party.  If his violence has also been directed toward the children and it has been continuous, then there is a potential that the court can restrict all visitation until he has taken steps to address his anger issues.

To make sure that your evidence gets before the court, it's always better to have a family law attorney help you.  Many attorneys now accept payment plans and most domestic violence shelters also offer assistance with custody issues that involve domestic violence.  If you simply cannot find an attorney, then you need to get together as many witnesses, documents, pictures, medical reports, as possible to show the judge that your ex-husband does not need to have custody of your children.