I’m not into gentle parenting - what’s the alternative?

I have an almost 3 year old who is actually a pretty good kid 90% of the time. I genuinely enjoy being with her on the whole. However. My mom is convinced I’m too lax and need to discipline her more, and I don’t disagree - when she tantrums or shouts a harsh ‘NO!’ it’s not great - she even sometimes tries to hit when she’s mad - and she’s at an age/developmental point that she’s often aware of her behavior and knows when she’s being inappropriate. She can clearly articulate about it all.

So here’s the issue. I don’t think screaming and yelling is the answer (it’s also not my personality). I try to do time out in the corner and it works temporarily but doesn’t seem to have much effect on her behavior long term. Anyone have other suggestions? I grew up with very harsh parents, and I’d rather not be as extreme and controlling with my children, but I also don’t want my kids ruling over me or the household. Sometimes I just don’t know how to respond in the moment and I’m very frustrated lately. (I also have a 4 mo baby so that adds to my exhaustion lol)

Edit: ok before I get the endless stream of gentle parenting is not permissive parenting, yes I know - so give me your very concrete steps of how to respond when a child hits you for example. “Holding boundaries” is a great phrase. But what does that specifically look like? I just can’t quite grasp how to put this into practice while also caring for my newborn.

And yeah, I’m going to hold that the examples of others I’ve seen who subscribe to gentle parenting (irl and online) are basically getting walked all over by toddlers. Maybe it’s not “supposed to” be that way but that’s how it often plays out.