The issue is probably of medical necessity. Your decree should define your requirement, however, in almost all cases, elective or cosmetic procedures will be excluded.
If constant filings are an abuse of the system, the court can require a party to submit pleadings before they are filed so that the court can rule on the issue of whether or not the "abusing party" can go forward. This is very rare as there is a presumptive right to be able to file most anything.
My colleague is correct in stating that the issue depends on the medical necessity of the procedure. If they are not medically necessary, they may not be your responsibility. Check with your decree to be sure. Often times because of the way Invisalign braces work they will not correct major issues such as overbites, but rather only minor cosmetic issues. You should consult a local attorney to help you investigate and fight the claim.
As far as the frivolous filings go, you can request an award for attorney's fees if she is taking unreasonable positions in her court filings, meaning she could be responsible for paying any of your attorney representation costs and fees. If the Court finds in your favor and forces her to pay your fees, she may think twice before filing a meritless claim again. However, preventing her from filing otherwise may prove to be difficult.
With respect to the constant filings, the best approach in my opinion, is to ask for an award of attorney's fees if she continues to take unreasonable positions or files unreasonably.
This answer is provided for general information only is not to be construed as legal advice. This response is not intended to create an attorney-client relationship.