Vampirequeen, I think we shared a daughter
. My #2 daughter had a tantrum in every shop in the village during the year after she was two, so, lucky granny that I am, I was prepared when #1 daughter's daughter turned out to be a very advanced child and began having them when she was about 18 months old.
I think the idea that it is partly frustration about not being understood is right. She was talked to in Spanish part of the time and English the rest and was not very early with speaking, which is common in those cases.
I had her for the day yesterday and, as she's had a tummy bug since Sunday night, my orders from her mum were to please bath her. We ran the bath, with bubbles in, found toys to play with in it, and then she decided not to have a bath. I offered a shower instead but no, not that either. I am not sure if it was our bath as normally we do it at her home and although she does fight sometimes she likes it when she's in. We sing songs and play. Her mum often says she has more fun in the bath with me, but that is so I bath her and save mum having to 
I finally got her things off and put her in but she refused to sit and screamed all the time I was washing her. I wondered if the RSPCC would come. No toy distraction or other helped so I just got her out, clean but very cross. She was still poorly though and only just eating bits of toast after 2 days nothing, so it was understandable. Luckily she is so lovely and adorable that the tantrums are worth it.