You hate seeing her upset op, that's totally understandable and evolutionary intended to ensure you protect her. But it's also your issue, not hers (I don't meant that to sound harsh). Crying is her voice and her only real way of expressing herself atm. She's okay with expressing her frustration/anger and you should try to be too. If she senses that you're uncomfortable with her emotions she will start to think it's not okay to be upset.
She needs to know it's okay to express her feelings and that you're there for her, not only when she's happy and smiling but when she's struggling, upset, frustrated, angry etc. And she needs to know that it's okay to feel all of those things.
She understands far more than she can say so I would start with a solid and consistent bedtime routine. Spend the hour or two leading up to bedtime explaining what it will be in lots of detail. And then follow through, reminding her throughout what's coming next, that's she's ultimately going into her cot and you will leave her to sleep. Be calm and confident so she can have confidence in you and the process. Be firm with the rule that it's bedtime so she's staying in her cot otherwise she will be confused by your getting her in and out and think she can get you to take her out again if she cries etc.
Once she's in her bed acknowledge her if she's upset, tell her you understand she's having a hard time with the new routine but this is how things will be from now on, tell her you're there for her if she wants a cuddle (lean over for a cuddle if she wants one), sing a song or two. Throughout the whole process remind her you'll be going after a set point she can understand (x song or whatever) and tell her your going to do something she'll understand so she can visualise it (wash up, tidy toys etc.) and that you'll check on her later. After the last song leave - it's torture for babies trying to get you to stay a bit longer when they know you're going to eventually go, so do what you've said you will. Of course if she hasn't calmed down after a minute or two go back, another cuddle, repeat the explanation that it's time for her to sleep and you have to do x chores (don't sing another song or you'll be in and out doing that for hours).
It might take a while the first few nights but once she trusts that you'll follow through, can confidently set boundaries and stick to them in the face of her protests she will have confidence in you and the routine and she will be able to be settle more easily.