S.H.
Well you can just, cold-turkey stop letting her watch tv. Sure she will tantrum. So what. Let her.
She will get over it.
At her Nana's... you can't control everything she does there. Or you can tell Nana, do not let her watch tv. Or, you can explain to your daughter- "You can ONLY watch TV at Nana's house. 2 shows. That's it." And let her SEE you explain that clearly, to Nana, at Nana's house.
For any Tantrum, or tearing up the house. You put her in time-out. Or, you tell her, each time she does that.... she goes to her room.
AND, take everything out of her room, that is dangerous or loose or can be torn apart.
Or you tell her firmly, the Rules. And just stick to it.
Right now... she is, controlling things. She knows, I'm sure, that you don't want to hear her tantrum. So you let her do things.
Or, you just suck it up. I mean, most ALL girls, LOVE "Princess" things. My Daughter did. But, it is a 'Phase." They will not like Princess things all their lives. By the time my Daughter was about 4 years old, she was over and about done with, Princess stuff.
The other thing is, you have things to do. Sure, like any Mom. We CANNOT play with our kid(s) 100% of the time. Its totally okay. Kids... also need- to be playing on their own and with their own ability. Because, if a kid is always entertained, they do not learn, how to be self-reliant.
Kids also do not need 'new' toys all the time.
Seems like your daughter is getting new toys and watching TV whenever 'she' wants. Then she gets bored.
To much turnaround.
You HAVE to be the bad-guy and tell her NO. You are not "bad." You are a Mom. That is what Moms, do.
She needs to learn how to play without being constantly stimulated by tv and new toys all the time.
I let my kids watch tv, but I tell them "I" decide what they watch. And when to turn it off. AND they will always ask first, IF they can turn it on or if they can watch a particular show.
We taught them how to assess tv shows, and I just tell them "certain shows are not good for you nor your age." That's it.
When my Daughter was only 4-5 years old... lots of her classmates were watching Pre-Teens shows. Already. Zack & Cody. iCarly. Hanna Montana etc.
But really, it is up to the parent, to decide, what show(s) a child watches and how affected by it, they get.
Find other things for your daughter to do.
If you don't want her to watch tv, then you need to put your foot down. Tell her No. Be the Boss. She is not the Boss.
You are the parent.
Also remember, a child this age cannot just be alone and do their own thing for long periods of time, while Mommy does her own thing. So you either do your things for shorter periods of time, or you use the tv as a Babysitter or you do things when she is napping.
No Mom... can 100% of the time, just play with their kids.
There are things to do.
Get your daughter used to.... other forms of entertainment.
Kids that age, like coloring, play-doh, chunky wooden puzzles, running around, pretend play, games, etc.
You need to start teaching your girl Boundaries/rules. Before she gets older and she gets more indignant.
From THIS age on up... any novelty or treat...can become a real big HABIT for a 2-3-4 year old. So, remind yourself, that 'their' habits came to be, because of what 'we' allow or not.
Once, I made the mistake, of getting my daughter a treat, after we took my Husband to work. Then, ANYTIME we took my Husband to work, my daughter "expected" a treat on the way home. It became, a 'habit', because of me. Kids, don't create these habits themselves. We do it.
It took me time and angst, for me to just get my girl OUT Of that 'expectational' habit.
all the best,
Susan