I think what's a bit odd - & the OP did say odd, not underhand or manipulative - is that MIL then went off without making any plans, saying the GC should 'phone her to fix things up. OP says they've never 'phoned her or shown any inclination to do so.
So now if this outing is going to be sorted out, OP's going to need to contact MIL again, or coach the kids to do the 'phone call, when it could all have been sorted out there & then. Not a big deal, granted, but a bit pointless.
OP could have been more direct herself, of course, & said - as someone suggested upthread - "Well, I don't have work to do, but if you'd like to take the children out, that would be great. When did you have in mind?" or something.
I'm guessing there are other issues here or a history of difficult communication. I do think that if MIL phrases everything in terms of her doing the OP a favour, that could be very grating. But OP hasn't given us any more info. so hard to know.