I actually can't believe some of the replies on here. All the people saying "You're CRAZY, of course it's totally normal for your MIL to be besties with your DP's ex and go on days out with her and lie about where she is, you're so controlling!" Are you all for real?
Ok, so the way I see it, you had some pretty extreme trauma in the past and you made it clear to your DP when you met him that you don't want any exes hanging around, which he readily agreed to, because, hey, it sounds like he has healthy boundaries too. He had already asked his mum not to be too pally with his ex because it wasn't a happy relationship - whether this is reasonable or not, she apparently agreed to his face and then continued bonding with his ex behind his back.
Now it's all come out that she's going for days out with the ex and HER new partner and buying presents for THEIR soon-to-be-born baby?
You could argues that it's "nice" she's being friendly (as many of the previous replies have) but it sounds utterly batshit to me. Sometimes we get on well with people but then they leave our lives for whatever reason, and we recognise that the closeness has run its course, accept that and move on. Interestingly I've noticed that "befriending the abusive ex after a break-up" is a pattern many toxic parents do, basically to piss off their children. (Not saying DP's ex is abusive, it's just fascinating to me that a parent would do this.)
All the posters saying you think it's nice to stay friends with your child's ex, would you also lie about not seeing them? And ask your new DIL to keep that secret from her partner? And praise the ex, to your child's new partner? You don't think that's completely toxic behaviour?
OP, you're not crazy, this is very weird. And I'm petty and childish, so I'd probably slip into conversation that you took your baby for a day out with YOUR ex-MIL, because you're still so close. See how she likes that!