Generally, during periods of possession, the party with possession has the following rights;
Sec. 153.074. RIGHTS AND DUTIES DURING PERIOD OF POSSESSION. Unless limited by court order, a parent appointed as a conservator of a child has the following rights and duties during the period that the parent has possession of the child:
(1) the duty of care, control, protection, and reasonable discipline of the child;
(2) the duty to support the child, including providing the child with clothing, food, shelter, and medical and dental care not involving an invasive procedure;
(3) the right to consent for the child to medical and dental care not involving an invasive procedure; and
(4) the right to direct the moral and religious training of the child.
Daycare would fall under subsection 1 of the above.
However, the court order may specifically address this issue, and require either notice to the other party, or consent by the other party.
If it does, one would need to comply with the court order to avoid a contempt citation. If the order does not make that specification, then the party in possession is permitted to make determinations as to who shall care for the child, and under what circumstances.
The court does prefer to see the parties work out any issues amicably, however, so if a change in daycare is anticipated, often times the parents will consult with one another to ensure that both parents approve of the situation. This is important because if one parent signs an agreement with a day care provider, and the other party disagrees, under the statute cited above, that parent can arrange for day care arrangements that suits that parent when that parent has possession of the child.
Under 153.133, the court typically will order that child care arrangements be addressed in the parenting plan. If it is not, one can seek clarification to avoid disputes in the future.