To be honest if my 3 yr old had been hitting, swearing, not listening nd endangering herself and others as much as that little boy, I'd be begging for help.
Yes children need connection, engagement and cuddles. They also need firm boundaries and consistency. Discipline doesn't equate to cruelty.
If I don't want my child to hit or run into the road then I need to teach her why its wrong and that includes showing there are consequences to repeatedly misbehaving. A baby doesn't know it's wrong to hit. A 3 yr old does.
And controlling emotions is part of learning self-control, learning to manage your own behaviour. Part of the early years framework I think? Would you encourage your 4 yr old to roll on the floor having a tantrum at school? Or act out aggressively? No? Then they better start learning to manage their emotions at 3.
And since when does an 18 month old need to be carried around all day (and is it even good for their development)? Sure it's natural and right to comfort them when they're tired/hurt/scared etc but at that age wouldn't they learn and benefit more from exploring/playing a bit more independently?
And no I don't perceive myself as dd's friend. I'm her parent and I'll always love and care for her as a parent, no matter what we spend time together doing. Our relationship will always differ from that with her friends. I wouldn't expect anything else.