God Northerner the selfish cow should be bloody grateful you graciously agreed to look after all their kids 2 weekends in a row, not start having a tantrum because you wouldn't do the 3rd FFS!
(never mind all the previous occasions).
"Disppointed in you" - how patronising.
And summoning you to her house like she's the lady of the manor and you're the maid or something.
I know you say you've agreed to go but frankly, I would call, not get into a conversation with her, tell her you've changed your mind about coming over and that you will write to her shortly.
Get back in that driving seat ! ....... how dare she be laying down the law when you've already bent over backwards for her so many times.
Then you write a very calm, mature and articulate letter to her expressing regret at the fallout. Explain that you don't mind being asked to babysit but you reserve the right to say no at any time as you also have your own life to lead. Apologise for anything you "may have inadvertently shared with MIL which has caused offence" and state "this was never your intention, however, you do not wish to become embroiled in a "who said what"-type of argument with her". For the sake of family harmony, tell her you hope this "misunderstanding" can be put behind you.
That way - she can't interrupt, she can't shout you down, she can't make you cry, it won't degenerate into a telling-off or resume of your "disappointing" faults. Instead, she will have to read your letter and you will have been able to get your POV across ...... in a dignified and "moral-highground" stylee.
Send a copy to MIL, so there's no doubt that you didn't send SIL a "nasty" letter.
It's then up to her how she chooses to respond - hopefully, she'll "agree" to "forget" the "misunderstanding" (Yes, I know she's a spoilt cow but you can't go down that route, unfortunately, if you do want to protect the brothers' relationship). If she carries on ranting and raving, I think you would then be justified in ignoring the silly bitch, SIL or not.