My toddler is only 1 but she got started on the tantrums/nappy change refusal early. At the start of that transition from lovely baby to angry bag of opinions, I started to lose it too.
I got it back again and this is how:-
Nappy changes: sing songs. "Happy and you know it" is the best because if you're clapping, you're not rolling.
I also say stuff like "well, it's time to change your nappy, so I'm going to lie you on the table and blah di blah and blah di blah" in this calming singysongy voice. If she's playing with a toy at the time, she can bring it up onto the table. 90% of the time, it goes ok. The remaining 10%, I keep breathing deep breaths and try to distract her gently from her plan to roll off the table.
Tantrums in general: I narrate how she's feeling. I say "I understand! You wanted to put the USB cable in your mouth but mummy put the cable on top of the shelves so you can't reach it, and it's really frustrating for you because you really wanted to chew it" sort of thing. Like, yeah, kid, life is hard. I get it. We're still doing it my way. Give her a hug and... boom. She's usually over it by the time I've finished chuntering on at her.
Avoiding show downs: give her a little heads up about stuff that is going to be a change of what she's doing "going to be brushing our teeth in a bit", closed choices "Do you want to put your trousers or your top on first?", routines up the wazzoo so things are more predictable for us both, picking my battles so it's not constantly me telling her off for being a toddler. Not giving her too much attention when she loses her shit, just give her a hug and put her down again.
Keeping my cool: mantras like "Share my calm, not join her chaos" "I'm sorry you feel that way about nappies!", "well, shit I guess I can try out for Parent of the Year award in 2019", walking off for a bit, gently massaging her when we have our (fleeting) cuddles and remembering how snuggles feel when she's being difficult. Noticing when my temper is running out and sort of doing the same routine on myself in my head "I understand, I'm getting angry because she's flipping out and making what should be a simple task three times slower while screaming at me for taking too much time. This is frustrating for me."
You know what you did was wrong and you're not going to do it again. So, don't worry about fucking her up. You'd only properly fuck her up if you did that sort of thing on the regular. We all shit the bed. It's ok to be good enough.