I would be inclined to try and parent her through the tantrums as best as you can without giving in. I have found a firm but kind approach the best when it comes to tantrums. Is she watching a DVD or the tv? If it just the tv, just wait until the credits run and then say 'it's time to say bye bye to the bananas now, they'll be back tomorrow' and both of you wave to the tv and then turn it off. When she starts screaming be really reassuring. 'yes I know it's hard when we have to say goodbye, it makes mummy sad too, but they'll be back tomorrow...now let's draw a picture of a banana in pjs instead...where are your crayons etc'. The idea is to validate her feelings but redirect her away from the tv.

I know tv is a trap with a new baby. For us it's play school. I let dd watch it on the computer sometimes too because it's hard when you're stuck feeding or settling the bub.

Good luck!