My guess is there was a phonecall where DH & MIL discussed how when it came time to leave you were lingering and the children were getting upset, because it appeared like you didn't want to leave.
In her view the children wanted to stay, this may be something DH shares, because you were unhappy you projected the emotions onto them. Which led to DH sitting in the car waiting and you dithering, obviously appearing unhappy, which made the children unhappy.
They might have discussed how MIL intentions were merely to give both of you time together, free from parenting. He's asserted that you weren't able to do much at all to utilise that time. MIL would have suggested the children were fine after a brief time, but what occurred upon leaving really didn't help the situation, leaving the children confused and slightly off.
DH could even have mentioned the argument on the way home, how you spent the night rather upset, with MIL asserting it was one/two nights. She ruined what should have been a relaxing time for DH and yourself. He then added how you said you heard her bribing the children into staying, which was point blank refuted, with an addendum if she heard that why wasn't I confronted.
The children had a great time, there was nothing to be concerned about. It's just a shame that this opportunity for free time was interrupted with theatrical hysterics.
DH has been left with the impression that you were being precious over the children, when it boils down to it he's a baby-maker / bread winner, you have no interest in him.
This is just assertions of course, but I can imagine it being turned from you being a mother missing her children, to something entirely different.
I hope you are able to sort this, I don't feel like you'll be able to put your foot down about MIL. But wish you luck, it sounds awful.