To be annoyed that SIL DD hurt my child.

[Mamabird2022]

backstory SIL has one child we will call DD1. DD1 is 2 years old, SIL treats DD1 like her best friend. There is no discipline at home which she openly admits too and says it’s her child so her choice. MIL has DD1 over once a week to visit and once every two weeks overnight. DD1 hits other children often which is why SIL stopped taking her to playgroups and instead takes her places where she can play mostly on her own.
Myself and DH have one child also who we will call DD2. DD2 is 9 months old. We visit MIL once a week and don’t allow DD2 to sleepover yet.

i was at my MIL house with my DH and DD1 was there on her fortnightly overnight stay when we arrived. We all were watching tv chatting and I was playing with DD1 while MIL spent time with DD2. My DH went to collect something for MIL at the post office and MIL had went upstairs. DD2 was sat on the floor watching tv and was playing with her toys that we had brought from home. DD1 was playing in the garden. A few minutes later DD1 comes into the livingroom where DD2 was sat playing and DD1 bends down as if she was going to give DD2 a kiss but puts her hand on her head and pushes her which caused DD2 to fall backwards and hit her head on the hardwood floor. I immediately picked my daughter up who was crying while DD1 was laughing. I shouted at her but she continued to laugh. MIL rushes down the stairs and after I told her what happened she put DD1 on the naughty step. DD1 kept getting up off the step wanting to play outside however MIL was firm with her and kept putting her back. The whole time DD2 was crying DD1 was laughing. About 20 minutes later my DH was sat on the sofa with DD2 when DD1 comes over to them. She took DD2 dummy from her so DH asked for it back as she had her own. DD1 then punched DD2 in the stomach and then began laughing again. DH told DD1 off and then moved her away from DD2. MIL was upset that DD1 was acting like this as she has never had any issues with DD2 before. We left shortly after as I was upset that my child was hurt not once but twice from a child who thought it was funny however SIL is now being funny with us because we told her child off for hitting ours. AIBU for acting the way I did?
edit the garden is completely enclosed and I could see DD1 out the window the whole time she was in the garden.
we all spent time with both children equally so it wasn’t like DD1 was left out while DD2 was there

You shouted her name probably in shock, I don’t think you did anything that bad OP sounds like SIL is overreacting. She might even be embarrassed or worried about something else happening that’s why she doesn’t want to have the DC around each other again.

Some children get jealous when a new baby arrives in the family. I'm sure they will be friends when their older. But for now if DN goes near DD just pick her up so she can't get to her. Got to be on the ball around children like this. Ignore the bad behaviour and reward when she's good. They often do it for attention if their not getting enough positive attention.

The aggression is totally normal. My DD is a big fan of the firm shoulder shove 😬

The laughing to me seems very strange based on the children I know.
When told off, my DD and friends tend to get a thunderous face and go for anger or sadness/ crying. they are now fully in the shoving, hitting biting etc phase which is all normal so lots of telling off followed by hugs at playdates 😂

Personally, I think your SIL has done you a favour... While 2 year olds will be 2 year olds the fact she can't take her to a play group indicates her behaviour is on the wilder side. Lack of socialisation by not going to play groups will only make it worse.

The sister in law is the problem here and I wouldn’t try engaging over her parenting style.
She will learn the hard way when her daughters older and she can’t gain control on discipline and tough situations because she’s raising a child that will learn that they can do whatever they like without consequences.
2 is a very tricky age and that’s why it’s important to instil boundaries which is down to her mum.
Keep your distance and visit MIL when SIL is not there.

Look I get why you are upset as SIL's reaction but realistically this was bpund to happen. A 2yo who is never told no and never disciplined grows into a monster 6yo who is never told no or disciplined, or a horrible spoilt 10yo etc etc. Think about that - this was surely always going to come to a head at some point when DD1 turned into a little monster and it somehow affected DD2.

Correct me if I am wrong but I don't know anyone who manages to have close relationships with families who refuse to discipline their child(ren) and stop it affecting the other kids in the family.

You'll find shouting at 2 year olds is ineffective. You need to stay calm and be consistent. Saying that you need to let SIL you will always advocate for your child until she's able to raise these things herself