I would be furious at the ex SIL!!! that's so mean.
Your ex MIL sounds horrid too, can't believe that she'd undermine your authority with the kids - what's that going to do for the kids but confuse them, cause unnecessary conflict and risk turning them into demanding brats (not that I think your kids are like that but if she teaches them to not listen to you and be uncooperative and unhelpful that's what you end up with)
Was she subversive like this when you and her daughter were together? I know my sister struggles with my mum undermining her discipline with her kid.