They can't force you to do anything beyond your ADSC, but the choices you're left with may complicate your personal life since you chose to marry an AD chick. I was join spouse for two assignment cycles. The first time, her functional pulled a rabbit out of a hat and matched her to a ground job near me, flying her with a local guard unit (drug deal). The second time, our good deals fell apart due to manning in the Viper world and her lack of IP-ness so we ended up matched to white jets.
If they can't get you a job in your MWS near her, they may offer you a white jet near her and try (seems like they've been successful lately) to stick you with the 3-yr ADSC for PIT. You don't HAVE TO take it, you could say no since PCS and/or training ADSC would take you past your UPT commitment. Overwhelmingly when I've seen dudes do this, the AF keeps them at their current assignment for the extra year, often with a 179 or 365 as a "thanks for your service" gift. I've seen a few rare cases where they PCS a dude anyway (to a location that doesn't require re-training/ADSC) and only get the ~1.5 years out of them there. For us Viper dudes, that means Korea.
BL - you'd likely end up choosing between (A) staying at your current base and (unless they can delay her PCS) apart from her until you separate, or (B) taking the PIT job and getting stuck with the 3-year ADSC.
Footnote - I was one of the lucky ones who got out of the PCS ADSC. When I PCS'd and went to PIT it was contentious but I signed the ADSC paperwork (adding 7 months to my ADSC) based on which battles I chose to fight. When I got to the UPT base, I called the ADSC office at AFPC and put it a magical trouble ticket based on the discussions above. Two weeks later, they whittled back my ADSC to UPT date. Looks like they are not doing that so much, coincidentally the shit has hit the fan with the pilot shortage...likely not a coincidence.
Edited to add: ThreeHoler is right - AD was more than fair to me/us when working join spouse stuff. Matching KC-135 and Viper wasn't easy; sounds like your match isn't easy either. That was your choice, not AFPC's.