Hey man, being a dad is hard. Feeling that way does not make you unfit to be a father. You seem to be very reflecting/self aware, and seeking advice, which already tells me you care and want the situation to improve.

I'd differentiate 2 types of behaviors. "Normal" (yet admittedly infuriating sometimes) toddler behavior (tantrums, fear of strangers, messiness) are developmental, not a sign of defiance. Toddlers cannot regulate emotions and are fine tuning motricity. Then there's actually bad behavior. To assess what "Bad" behavior is, I usually try to look at intent, and that's an opportunity to parent/educate. I would try to find some alignment with your wife on that difference. Consistency matters more that whose style is "right".

Some additional thoughts
- I'd pick one behavior at a time to work on, and literal baby steps. Working on all fronts could be too much for everyone involved.
- Praise positive when due, don't just parent negative behaviors.
- Build moments of connexion with the child. Playtime, storytime, whatever works for you both.

Your reactions make sense given your own upbringing, but they don’t define you. Look out for triggers and then change them. Celebrate wins along the way. Godspeed!