You actually sound like you're a genuine person and have good intentions with her. I don't know whether it's the way you're phrasing it but it kind of sounds like she's got some highly strung personality and it's almost impossible to deal with. I can relate to her because I am pretty much on edge all the time due to commitments as well, and I would take it out on other people close too, but I would afterwards be aware I was doing that, and I would usually apologise for the way I was acting.

While I definitely can understand why she would get upset if you were aloof and disinterested when meeting with her, it seems like she has serious issues, and feels like she is being victimised.. I can also see how she would be upset if she met up with your friend and then you acted in a way she was displeased with, but she seems to have taken it as a personal attack directly at her?

I can only really come up with 2 ideas, and one is that she is really interested in you but feels like you don't show enough interest (with your aloofness) or your actions aren't acceptable, so the pulling away is kind of like a method to try and get you to show more interest/beg/apologise for what you did; it is a little manipulative but it does make you think and run back towards her (alternatively it could make you walk away completely). The other possibility is that she isn't particularly interested in you, which is why the moment you do something slightly wrong (even if it is not a personal attack on her), she finds it easy to 'punish' you by pulling away and acting hurt; perhaps each time you 'screw up' she questions whether you are right for each other. Then again, perhaps this is just her detached style to disappear for days at a time, and she is the one being aloof..

Again I'm not saying she's totally in the wrong, because I can see how some of your actions may make her feel unhappy and a bit rejected, but from what I can tell her reactions seem to be a bit extreme for the circumstances? Just my opinion though I may have misread/misinterpreted. I think if you really truly care about her then you should try to fully understand how busy and stressed she must be from work, accept that her feelings of hurt are probably genuine, and try to be her rock for whenever she needs it. But also be prepared to walk away if it seems like no matter what you do, you will be blamed anyway.