Talk to her dad calmly. Tell him that you both need to be on the same page about discipline and since you won’t hit your child that’s not an option.
These are what I use, most things don’t need punishment and just need some guidance. If my daughter throws something on the floor I say “hey violet if you’re all done can you throw it in the trash?” And I’ve been doing that since she started walking and ofc impulse control isn’t developed yet so she’ll dump her cereal then just help me clean it up or she’ll dump a drink but anytime I do something I just demonstrate the reaction I’d want her to have
I personally don’t agree with hitting a child. I go with talking for sure and time outs. Toddlers are hard and take a lot of patience but it works way better in my opinion and keeps a better relationship in the long run. Personally I would step in and not let a man hit or smack my child.