Yes, FSA funds can be used to pay for medical expenses incurred by spouse and dependents (so long as the dependents have little to no income and can't be claimed by another).
However, her FSA apparently makes you ineligible to contribute to an HSA. According to this HSA FAQ from WageWorks:
Even though you are not covered by your spouse’s health insurance, the
IRS has determined that your spouse’s FSA is considered “other
insurance” that makes you ineligible for an HSA. An exception to this
rule exists for limited purpose FSAs (those that cover vision and
dental expenses only) and you would be eligible for an HSA if your
spouse had a limited purpose FSA.
I'm not sure if it could be simply rectified by stopping contributions to the FSA or if it would have to be closed out entirely. The whole idea is intriguing so I'll likely research more later and update.