If the court orders the home study then the court usually appoints the evaluator. Additionally the evaluator will examine both homes for his report.
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Unfortunately, home study and fast are two things that don't happen. With your distance, you're likely going to have to do a private home study because I doubt Dallas County officials will drive out 6 hours. If they ordered you to do the home study in Dallas, pay the fee and get rolling ASAP. If they ordered you to do a private home study, get rolling on that one (it'll be more expensive but happen faster).
If you do not do the home study, you're going to have it found against you which is very, very bad for a custody battle.
The best thing you can do at this point in time is to pay the fee, use all your visitation and if need be, consider moving closer to Dallas.
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