You've had some really good advice from posters.
You are not a failure, at all. This is a very hard task at the best of times.
She's not coping well, 8 is still so little. You've recently moved in together and she probably sees this as more permanent in her mind, and a threat. She'll be worrying she's losing her dad.
The tantrums, and not being able to make decisions point to a vulnerable child. So is the need to be on a screen. This is a coping mechanism.
Things will work out with careful nurturing.
Can you reach into her world and join her with a screen game, multiplayer maybe? Mine craft is ideal for this and you can build things together, you don't even have to be in the same room.
I became a facilitator for Dad and exW.
Blended into the background for a bit.
Tell your DSD how wonderful her dad is, lots of praise. Always smile, I know it's hard. Tell her how glad you are they can spend time together and that its special.
Take time to tell her positive things about herself to boost her.
Speak positively about her Mum, even if it's difficult.
For example when I made biscuits with my step children I always slanted it towards making some special ones for Mum and getting them to package them (as an activity).
If you are out maybe let her chose a little something for her Mum.
Encourage photos of all of her family. Make her space in her second home her own and special. Maybe a pull away bed if she wants a friend to stay over, even if it's not used it sends a message that her friends are welcome too. I appreciate this may be a while yet.
it's not your job to mother as such, it's your job to help her parents raise a happy healthy child.
If she was having some time with dad, I might pop into which ever room they are in, and comment how lovely it was spending time together and bring them drinks.
With my now older DSC after many years it's reaped rewards. The children rush in to talk about their day, ask if it's their favourite meal I'm cooking. They text me when they are not here. They seek me out to partner them in computer games.
I also didn't vanish, if they were in our lounge I would be in the same room on a different sofa.
If we went out, we all went out. But don't be afraid of getting out and doing something for yourself if you need space.
I think the other thing that occurred to me is children rarely appreciate or understand the behind the scenes work you'll do. The fairies cook, clean, make beds and hoover. So if, In your mind you're doing a lot for them. They won't see it as this. It's very normal for it not to even register.
The bits they see and will respond to are the smiling and the positive comments.
Our motto is 'Happy, healthy and precious'.
Best wishes, it's a hard one to crack.