My Rule on TV has pretty much been the same since they were little, if I don't want them to watch TV *I* need to be the one to provide a suitable alternative, if my alternatives aren't taken up (cooking, trip to park, helping me with chores, playing in backyard etc) then I will let them... it did mean that when DS2 was born DS1 watched way way too much, but now as a 7yo he only watches about 4hours/week & that is sport.
I also think there is nothing wrong with a child being upset when they don't get what they want, as long as that upset doesn't get the parent to change their mind... IMHO I think expecting children to "suck it up" & not be upset is more unreasonable than them asking everytime they think "Umm I wouldn't mind watching TV"
TBH I think you have to work out in your own mind whether your issue is her tantrums or your desire for her not to watch TV, because (annoying as it is) we can't always have it both ways... stick to your guns & accept the tantrum could be a result or want to avoid the tantrum, then maybe you need to lessent the standards. Because at end of the day the tantrum annoys & frustrates the parent but it is a "normal" & reasonable response from a toddler & better to have the frustration out than bottled up.