@Allthewineandallrhedrinks To be honest I don't think you have given us enough to judge fully.
On the face of what you have written, and I confess to not having read it all, you haven't disclosed what your husband said to your niece except his Mum told him to apologise, so it can't be nothing? So unless we know we can't say if SIL was justified in storming off to the bedroom.
But what you have told is that you rang your brother about Easter hence prompting a confrontation by telling him " because your wife is a toddler sulking off and we don't want to see her again" and that was never going to get a positive outcome, you lit the dynamite intentionally there.
You could have text and made an excuse for Easter, or if you wanted to truly resolve it, you could have explained how unhappy you were with how your SIL reacted given it was (potentially) a misunderstanding or over reaction by the niece and cleared it up in that manner.
I'm assuming that your SIL is married to your husbands brother or is she married to your brother? If its your husbands brother I am sure he would not be happy his wife is stirring the past up over his brother either if he knew. If its your brothers wife as I am assuming from the post, then its still not nice. But I am pretty sure a reasoned woman would not intend it to hurt any children involved and by the reaction from the school gate mums, that is potentially what it has done. One thing that is clear is that the women at the gate are not your friends, they would have talked to you about what was being said before taking any action.
You don't want to say what your husbands criminal history is except it wasn't sexual and I get that. What your SIL has done, has potentially caused issues for your children at school because many people are very careful when it comes to who they and their kids associate with and despite what they say, don't believe in 2nd chances. That's wrong, but did your SIL intend this? I doubt it and I think she would be mortified if she knew the situation.
But you are not innocent here, you set off like a heat seeking Exocet missile homing in on your target by ringing your brother and saying you wanted nothing to do with her, you made no attempt to resolve, you went for the jugular. How you describe her reeks of jealousy. Actions have consequences.