I do think there are solutions in between "suck it up" and "let her cry". FWIW.
She's 2 so she should be starting to get a bit of language and verbal understanding to play with, which will be a huge help.
There is a nice book called The No Cry Sleep Solution for Toddlers, which is helpful if you want to change things but can't deal with crying based sleep training measures. Lots of useful suggestions in there. I haven't actually read this one but I've read the original No Cry Sleep Solution and the Newborn one and both are very good with plenty of suggestions and troubleshooting.
And yes, I think there is a sort of split between those who consider sleep training and those who don't - but not sleep training doesn't mean you just have to live with things that are making you frustrated until they magically grow out of them - you are allowed to make some changes that benefit you! I personally wouldn't do crying type sleep training, and I wouldn't do rapid return, although by all means try them if you think they are the right thing. For me it's just more about either a two way communication if they're old enough to understand and handle that, or trying to gently stretch the boundaries of what she's comfortable with a little at a time so that she's not getting distressed, and therefore expanding your options in the longer term. It doesn't have to be a battle that only one of you can "win", and I'm not comfortable personally with "training" methods that involve leaving a child in distress, even though all of the following ideas could absolutely come under the heading of sleep training, so it's a bit fuzzy.
Sleep is going to happen when they're tired, relaxed, comfortable and sleepy. As she is eventually going to sleep with you present I don't think tired, comfortable or sleepy are the problem, so it's a question of can you get her to relax without you there. The way you describe her jumping up as soon as she thinks you are leaving in particular makes me think she's not especially relaxed about the idea of you leaving, indeed, she's quite anxious about it. So I'd try a couple of different things out just to see if you can get anywhere with them. The idea with both is to gently get her used to the idea that you can be there for her without necessarily being right there by the bed.
First of all, when you've been there for a while but you know she isn't close to sleep, let her know that you're reeeeeeeally desperate for a wee and you need to run and go for one, but you promise to come right back. Use whichever words/phrases you think she would understand the best. And then leave, do a wee (if you like) or just count about 30 seconds, and then go back in. If she does cry, it's less than a minute, and you might conceivably have needed a wee! If she's calm when you get back then just continue exactly as you were before, whether that's reading stories, stroking her back or just sitting quietly. If she's upset then start off just saying something reassuring without picking her up, and if that doesn't work, restart your initial calming methods to get her to go to sleep. Try this again, not on subsequent nights, but randomly to see if she adapts to the idea that sometimes you leave, but you always come right back.
If it works: Try it at different times, like when she's almost asleep. Try leaving for longer or telling her different reasons that you're leaving, especially as she gets older and increases her understanding. Eventually using this technique you should be able to move to a state where you tell her "Mummy has to go, but I'll come and check on you in half an hour/an hour/after dinner/when I go to bed." And she will be fine with this.
Second: Try experimenting with where exactly you sit in terms of distance from her. Ideally you want to find a point which is similar to how she felt about not having milk on that first night - where she's OK but not totally happy or comfortable with it, but not distressed either. Reading the books from this new, further away point is a good idea. Keep that as the new routine until she comes to expect it and is totally OK with it at which point, do another move further out. Eventually, you'll sit just outside the door, which after one successful night you can just leave. Other people have mentioned gradual retreat which is similar, also disappearing chair.
Third: Try weaning her off the stories by stopping reading when she is a little less sleepy each night with the idea being that after a while you read one story and then sit, and long term that you read one story and then leave. Along the same lines of "stop breastfeeding while they are still drowsy but awake" - I have never had any success with this one ever. But you can try it.
Fourth: As her language and communication grows, try suggesting other sources of comfort to her. I don't think you will be able to do this quite yet (although she might surprise you!) but it will be something she might be able to understand better as she gets older. Explain that mummy/daddy is very busy tonight and has to go and But would she like to snuggle up with instead? And mummy/daddy will come and check on her later. OR "I'm too tired to read you a story tonight, but would you like me to put on a magic story instead?" Play an audio book, you can get CDs or MP3s, somewhere out of her reach in the room on very low volume so that she has to lie still and not rustle the covers to be able to hear it. Stay if you like, maybe to attempt the disappearing chair idea at a future date, or introduce this if she's having trouble with you leaving when attempting one of the other methods.