It could be a bit of both? They do seem to be naturally defiant at this stage, just getting through it, being consistent seems to be the most important thing, so keep at the routine you want her to have and it will eventually click . Try and make sure everyone else does the same too - so CM and any family all get on board.
Sometimes you might have to give in, there will always be disruptions, but try and re-establish the routine, and keep going with it, always be prepared to distract her from bad behaviour whatever way you can (my favourite distraction technique is tickling ds, he loves it, but not all children will, and only before he escalates to tantrum stage). I went through a phase of having a stash of interesting little toys, that are rewards, you could have them visible on a high shelf, so they are only available to choose when the child does what you want. Things like bubbles, squishy things, anything in a wee bag - ds would get one of these after doing something - I was all for bribery, even something tiny like a chocolate star would work... but put them away at some point so they still are interseting, or keep adding to the stash - pocket money toys from hawkins bazaar kind of stuff.
I also tell him in x minutes we are going to do this (i.e get changed/brush teeth/stop watching or playing on the computer) and I stick a timer on (sand timer or I use my phone) it helps him prepare for the change. I think he is better to deal with when I limit his screen time - so if he plays on the computer it is for 30 mins max - though sometimes I let him have more time and know he will be grumpy, but giving him a 5 minute, then one minute warning helps him, and he does sometimes come away himself now, because he is used to this.
I also had whatever age he was time limits so at 3 I would expect 3 minutes attention, extending this with age, so 3 1/2 minutes at 3 and a half years (I would do time out like that too - though time out was actually time in another room, with me sitting quietly ignoring him - because time out turned him to frenzied panic - I couldn't leave him).
Have you heard of the backward step method? chaining method and other tips there, might help.
It can get better, but it is sooooo hard, I remember a lot of tears (mine) and heartache. It is so stressful - try and make sure you get a break too, it is hard for others to deal with your child's behaviour but it is good for the child and family to learn to deal with it - helps them create those bonds. Remember to praise your dd when she does anything, no matter how small that is good - big celebratory dances, cuddles etc whatever works.