So basically you're finding it hard to say "no" to your kid when you think they've enough screen time, or you don't like it when they get upset that you tell them they have to eat their veg/go to bed?
Suck it up. You're a parent. You need to be setting boundaries and rules. Look for different ways to get her to eat her veg - doesn't want to eat broccoli, ok ask her to pick which veg she wants instead. But make it clear, she has to eat x amount of veg.
Put a clock up, or a timer on so she knows when to expect screen time to end. Or give a 5/10 minute warning rather than going straight to "switch off". Find something else to do after screen time that she looks forward to perhaps? Or set a routine.
Maybe make it that it's screen time after dinner only if she's eaten her veg?
Bed time tell her if she doesn't go to bed, the next night will be 15 mins earlier, and the following night 15 mins earlier again until she starts going to bed on time. Make sure her bedtime isn't too late that she's gotten over tired. Have a strict no screens in the bedroom rule. Get her involved in picking a bedtime story to read.
But be the god damn parent. Your child NEEDS you to parent her. You don't show her rules, boundaries and consequences, what happens later in life when a man pressures her into sex because it's what he wants and she's only ever seen demonstrated that you never say no?