The mother and father of the child have been to court before. The father legally has the child every Thursday, every 1st, 3rd, and 5th weekend of the month, and various holidays. The mother wants to leave Texas to go live with a family member in Illinois, citing "financial hardship." Can she legally do this?

Not without the court's blessing. The court isn't about to force dad to travel interstate for visits without at least letting dad have a say, or even a shot at custody himself.

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I agree. She would need to get permission from the court. Have you browsed through the information in LawInfo's Free Legal Resource Center to learn more about your issue yet? See: http://www.lawinfo.com/consumer.html. You can certainly try to speak to a lawyer to determine what legal options may be available. In the meantime, you may be able to learn more on your own. Search the "Free Legal Resources" tab, or browse the Consumer Resources. Good luck.