I feel you on situation #1; I have to force DS (24mo) into his car seat with some regularity, maybe a few times a month. He is limitedly verbal and obsessed with playing with the buttons on the dash. My best (and really only) tactic is to fully engage him with song, play, stickers, look-at-that-bird, as I'm putting him in. That's probably unhelpful for a 3 yo though. Like others have said, I've found that if he's in refusal mode and I see that I'm probably going to have to physically hold him in the seat and strap him in, that I stay calm and neutral. It's so easy to go to the red zone with them, and it's never productive.
With your food situation, she's definitely caught onto the power of food...I wonder if you could starve the power a bit? That would be my approach, anyway. Even if she only eats a bite, don't comment on it. I wonder if your warnings to her that she'll be hungry later is only an invitation for her to try to prove you wrong, or maybe she is needing to reaffirm that she is in control of what she puts in her body, which ultimately, she is. But then, she DOES end up being hungry later, and double bonus for her, she can use it as a bedtime stalling tactic.
So, if it were me, I would just halt all commentary on food consumption. If she only eats a bite, I'd clean up the kitchen like usual and just stick her whole plate in the fridge. Then if she's hungry later, I'd pull it out and set it someplace she can reach it so you don't have to sit right there with her. What we often do for DS if he doesn't eat much at dinner, is we just transfer his plate from the table to a chair, then he's free to pick from it throughout the evening if he likes. If/when she does request more food, I wouldn't comment on that either, no "I thought you might still be hungry, you didn't eat much earlier" or anything like that.