A plan participant's spouse got sentenced to 125 years in prison. She wants to change her beneficiary designation to her children. The spouse in jail will not consent to waive his benefits. Does she have any recourse other than divorce?

This sounds like one for the lawyers.

While divorce isn't necessary, legal separation or a court order showing the spouse has been "abandoned" is.

You would need to obtain a Qualified Domestic Relations ORder (QDRO). do not have to be divorced to obtain, but requires issuance from local domestic relations court.

I disagree. The spouse in jail can seek a QDRO (if he can get one from jail). But, if there's a judicially recognized separation, the employee can designate whoever he or she sees fit as beneficiary, unless a QDRO provides otherwise. (See 1.401(a)-20, Q&A 27, but make sure your plan document is not more restrictive)