Generally, no, because 50/50 possession and access is not in the Texas Family Code. Most people who have it, got it via agreement in mediation. Expanded Standard Possession Order is the closet to 50/50 in Texas.
Yes, if two conditions are met. 1) The child must be disable and unable to provide for his or her self. 2) The disability was known at the time the child was a minor. Tex. Fam. Code § 154.302 (a) The court may order either or both parents to provide for the support of a child for an indefinite period and may determine the rights and duties of the parents if the court finds that:(1) the child, whether institutionalized or not, requires substantial care and personal supervision because of a mental or physical disability and will not be capable of self-support; and(2) the disability exists, or the cause of the disability is known to exist, on or before the 18th birthday of the child.