In theory it should have been lovely but it ended with a heated argument and tears this evening because she didn’t want to go to bed (at 10pm).
Don’t write off the whole day because of bedtime tears (or a bit of bickering, or a bit of a huff) try to see it in its whole, you did things as a family that your DC would enjoy and your DD didn’t want to go to bed. In your mind you’ve given her a lovely day and 10.00pm is a reasonable bed time. In her mind you’ve ruined her day by imposing a bedtime. Both of you are right!
Try to give her 1:1 attention, set clear boundaries and communicate them, eg I always give my kids a 10 minute warning about coming off screen time, I’ll tell them when bed time is and what’s happening between now and then etc. Give her the chance to redeem herself, if I remove screens from my DD, I’ll also agree a way for her to earn it back again by doing chores, behaving well, not fighting with her brother. It works because there’s always a way back from whatever behaviour.
Please don’t try to involve her in caring for the baby or spending time with her unless she wants to, if she’s feeling insecure, there’s nothing worse than being forced to interact with the person that’s causing your insecurity. Let her build a relationship with her sister in her own time and in her own way.
Lastly, look for the good in her - when she’s at her worst, remind yourself she can be funny, caring, thoughtful, entertaining. When you’re having fun together tell her how much you like spending time with her (not “I live spending time with you when you’re good, kind”, just “I love spending time with you”). Let her know she matters, be explicit about it, praise generously - even if she squirms, she needs to hear it and it’ll help take the edge off your annoyance with her.