I don't dance at all. I passionately don't enjoy it.
DS isn't married, not even close but I already have nightmares about this. [Doesn't help that he says he wants the Time Warp
] What you are saying they want to do would be a 1000% no from me, not happening, I wouldn't blink with that no. And yes I'd show up in a boot if I had to. I'm thinking because DIL is a professional dancer she of course would think this was fun and unique to weddings but special to her. It probably never crossed her mind that this would be upsetting to someone else to be put in to this position. I absolutely wouldn't worry about the Mom - she'll get over it and it will be in the past (sounds like her personality is ongoing so nothing will stifle that). I would sit the couple down and just tell them that what is being proposed is very stressful for you and it's not something you are comfortable with. All weddings are up for adjustments so let them start the dancing without you. Tell your son you would like a song you all picked to be played later in evening and you two join the dance floor together. Your family might notice you having your special time but honestly it's just for you and your son anyway. The rest will be oblivious.
Changes to tradition are okay. DD insisted that the best man and maid of honor toasts be done at the rehearsal dinner. She didn't trust MIL to not try to hijack the mic at the wedding and speak. So DJ was informed father of bride does his welcome to all and speech, then the mic was locked down from anyone else. No one noticed and it worked out just fine.
On a positive note it sounds like DIL is more like your thought process than her Mom's, that is a good thing. She has grown up with her Mom and likely finds some things just easier to go along with and then like all weddings, it will be in the past. Hopefully they find a way to balance the important things in life to reflect what their needs and desires are.