The disabiity standard for SSDI and SSI is essentially the same. She must demonstrate an inability to perform any "substantial gainful activity".
However, SSI is more in the nature of welfare for the disabled. Consequenlty, if she has other income, including earned income, that could partially or totally disqualify her from SSI payments. In that respect the SSI program is different than SSDI. Benefits for SSDI do require that the person have enough recent credits under SS and is computed on the average earnings (oversimplified explanation) under SS before becoming disabled. However, Bill Gates could potentially qualify for SSDI if he could supply the necessary medical evidence. SSI has no such requirement of recent work credits under SS. . SSI benefits generally are lmuch ower than those under SSDI.
SSA does not require vocational rehabiiltation of anyone in either program. It offers these services, but they are not compulsory.
I think trying to prove that she can work is going to require an independent medical evaluation, or multiple such evaluations, etc. I just don't see a family court judge ordering such. I might add doctors do not work for nothing. Someone would have to pay for them. If they have to testify, then someone really has to pay for them. It will not be the court and I don't see a judge ordering someone on SSI to pay either.
If you want to discredit her, given that the benefit is SSI, I would try to see if she has an income source, other than child support, that she is not reporting to SSA. Medical opinions, as you have discovered, can be subjective and hard to refute. Yes, I agree that it possible to game the system. (See the workers' compensation system for numerous examples of this issue.) But, if she is working under the table or has other income, including alimony, that well could have a bearing on her entitlement to SSI.
Please note that child support is for the benefit of the child /children and likely will not be counted against her.
Please note that while SSDI payments, because they generally are higher, can be garnished for child support, SSA will not garnish SSI payments. So, even if you managed to overcome the other obstacles, if the only income source that you could identify was SSI and you were attempting to collect from her, you likely would not be very successful.