I'm an "above-average" Starbucks employee. I like to wear a judge's robe while mixing Java Chip Frappacinos.
Anyway, the issue is entirely controlled by your court orders, which almost certain have a provision for unreimbursed health care/medical costs. The court is required to order, under TX Family Code 152.183: "(c) As additional child support
, the court shall allocate between the parties, according to their circumstances: (1) the reasonable and necessary health care expenses, including vision and dental expenses, of the child that are not reimbursed by health insurance or are not otherwise covered by the amount of cash medical support ordered under Section 154.182(b)(3); and (2) amounts paid by either party as deductibles or copayments in obtaining health care services for the child covered under a health insurance policy."
Assuming that the court has issued the required orders (which sometimes does not happen, so read your orders carefully), then you are liable for a portion of the "reasonable and necessary health care expenses...not reimbursed by health insurance."
So, the issue boils down to whether or not the chiropractor's care was reasonable and necessary "health care." This is highly arguable -- because there is no Texas appellate case law interpreting the question definitively.
In TBCE v. TEXAS MEDICAL ASS'N, 375 S.W.3d 464 (2012), the court of appeals throughly dissected the difference between chiropractic and medical practice. And, while the court held that chiropractic is a specific type of care, which permits diagnosis and treatment of "subluxations," the court also held that chiropractic practice is in no way the practice of medicine.
So, the question, now, is whether or not "health care," for child support purposes, includes chiropractic care. I would argue that it does not, and moreover that despite the government licensure of chiropractic practitioners, the entire study of chiropractic is entirely outside of the scope of methodical naturalism (i.e., "unscientific").
Assuming that the court agrees with your argument (something that I cannot predict), you are not liable for chiropractic care for your child, because it is not only not reasonable or necessary -- it's not health care at all.
Note: My apologies to any chiropractors who may read this. I am making a legal argument, not a condemnation of a well-established industry. There may be many people who find chiropractic care to be extremely useful. But, there are also many people who find that stock market technical analysis is extremely useful -- despite there being no scientific evidence that demonstrates technical analysis works any better than throwing darts at a page of the Wall St. Journal.
Please let me know if my answer is helpful. Thanks in advance.