Two things I noticed here: Firstly, the issue of the assault. BIL1 is extremely lucky you didn't call the police for what he did to a 4 year old child. I think PPs have covered this, so I won't go over again.
The second point I noticed is that you say MIL 'isn't taking sides'. I think that is completely untrue. She is taking sides and is supporting BIL1. Otherwise, she wouldn't be expecting her grandchild to be in the same room as a child abuser and wouldn't be expecting all of her sons at the same party. If my relatives acted like this, I wouldn't invite everyone and leave it up to the victims to decide if they could stand being in the same room as the offender; I'd take the latter off my guest list for the comfort of the people he assaulted.
I have no idea why your DH is trying to apologise/reconcile with his brother (I'm really sorry you felt you had to assault a 4 year old - it's all his fault, we'll watch him better next time? - does that really make sense to you?). If this was me, I'd be having nothing to do with this person until he made a grovelling apology. I suspect the PP earlier who says that in dysfunctional families, one person has to be the 'reasonable' one (read doormat) is right and your DH has been assigned this role.
Also, does anyone have anything except BIL1's word for the fact he is on medication? IMHO, either the family doctor is a quack or BIL1 is lying - drugs like that should only be prescribed by psychiatrists (although I accept things may be different in the US).