Man, I remember those days. Basically doing the same routine is boring and they don't see why they should bother, they want bodily autonomy NOW!
Things that might help:
Start bedtime routine earlier. You want to catch her before she's overtired. Allow an hour before her actual bedtime.
New bath toys. If you're short on cash then this could be using your colander, empty bottles etc in the bath or toy animals that won't go manky.
Also on the bribery front - bath bombs, squirty bath foam stuff, bubble bath in an overpriced TV character bottle that you can then refill.
Try showers every now and again instead, my DC find it hilarious to be tickled by the water.
Always follow the same routine more or less, easier said than done I know. I think they find it comforting after a while.
Try the odd daytime bath on a weekend so she doesn't always associate it with bed. Good way to spend a rainy afternoon!
For teeth - mine like it if I spot things they've eaten on their teeth and scrub them off, or sometimes other things like the gruffalo hiding in there or pirates. Anything to make it less boring.
Tell her stories while you're doing it.
Give her more of a role so putting the bubbles in the bath, pulling the plug, putting on her own pyjamas etc.
Re stress - not easy. You build up resilience (I have a 4.5 yo and a 2yo) I am much better able to keep my cool than I used to be, mainly because I have realised that losing it is basically a time penalty because you have to soothe DC about you losing your temper then still sort them out as you would have had to initially!
Sometimes I focus on what I can see, smell, hear, touch etc, take deep breaths and try to feel in the moment. Kid is freaking out right now. It won't last forever, I need to get from this point to the point where the tantrum has ended, that point will definitely come, what do I need to get there?
It can also help to avoid clamping down on those feelings. They've had a long day, they have feelings to get out, make space for that to happen and don't always try to jump on it and put the fire out. Say things like 'oh, it's been such a nice day with lots of exciting things, hasn't it? We'll have lots of fun tomorrow as well' or 'are you a bit frustrated about your toothbrush? let me help'
Conflict and stress will escalate when you return her tension with more of your own. Being relentlessly positive can help to defuse things. So rather than 'no, you have to have a bath now!' you could do 'it's so nice in that warm bath, do you think you can hide your toes in the bubbles' etc
Try not to get caught up in the heat of things - sort of soar above the situation like an eagle so instead of 'why won't you bloody put your pyjamas on' see it from above - she's tired and wants more cuddles, maybe I can cuddle her or sing a song while she puts PJs on.
I don't know if any of that is helpful or contradictory! It's a general mindfuck. No bad kids by Janet Lansbury is worth a read, or the whole brain child, or how to talk so little kids will listen.