advisor - Problem with undergraduate research supervisor, how to proceed?

Setting

I am currently an undergraduate student in chemistry and I have recently started working on an undergraduate research project in a known laboratory in the US. I am very passionate about the topic, however I have problems with my supervisor, who is a PhD student.

Problem description

When I came to the lab asking for a topic to work on, the Professor assigned me to one of their students, which appears to be common practice, so I did not question this. However, I found out later that my supervisor (the student) was the only person in the lab working on the topic, and that she herself had only started working on it not long ago. After several days in the lab, my supervisor has not revealed what the eventual goal of my project will be, and from the way she behaves (stressed out, impatient towards me asking questions, which is an additional problem), I suspect that she might not know herself (quote: "we'll figure out along the way"). This is severely frustrating. I am aware that research is an open-ended endeavour that might be changed as new situations arise, but I thought that undergraduate research should be something self-contained, with a clear goal and time-frame, and usually well-thought out by an experienced researcher? I am aware that one possibility to resolve these issues could be to simply talk to my supervisor. However, there appear to be some barriers, which leads me to my question.

Question

How can I approach the situation without ruining my standing in the laboratory and appearing like a complicated student, even though I am not? I would love to continue on this or a similar topic in this lab, but the current situation is very unpleasant for me.

I feel like I cannot talk to my supervisor directly as she seems impatient and stressed out, and at the same time inexperienced with supervising undergraduate students. I fear that this could make the experience even worse, with my supervisor getting angry at my criticism.

The other option I can conceive of would be to talk to my supervisor's supervisor, and ask for some kind of intervention from above. But this could also backfire in many ways, possibly making me look complicated and unwanted in the lab altogether.

Answer

I'll be honest with you, remarking that this is only my opinion, by no means I'm right.

Undergrads are a pain to supervise.

Mostly because, in general, undergrads require a lot of "hand-holding" and training (proper research procedure and writing are not usually covered before that), which takes time (even worse if it is a good student that challenges you.... rewarding, but takes even more time).

You are right in thinking that undergrad research should be simple, self-contained, and well planned out. Properly planning stuff takes time, professors never have it. And simple means that the research is unlikely to have high impact.

I know several professors that don't accept undergrads simply because they think it is not worth the effort. The ones that do accept, pin them to a Ph.D. student (or a postdoc) and that's it. The Ph.D. students usually are busy, worried about their own things, and do not have the experience to deal with "underlings".

Yes, your project should be well defined, with clear goals and schedule. That never happens. Not as an undergrad, MS, Ph.D., postdoc, or professor. There might be a few unicorns around, but, usually, you have no idea where you are going. Ideally, you could use this opportunity to train the most important trait in a researcher: independence.

Instead of expecting to be handed goals and schedule, create them. It will be challenging for you, but you would learn how to do it, and get familiar with the field. Then you could go to the Ph.D. student and ask "Do you think this is a reasonable plan?" instead of "what should I do?". Worst case scenario, that plan can be a starting point for a better one. Bonus points if you include solutions to tangential problems of her research (stuff that would be cool/easy to do, but isn't a priority, so she would never do it herself).

Quoting a far better man, and professor, than myself:

"Be honest, be kind, be useful, be responsible, work hard, treat everybody with respect."

I'd advise you to go around the Ph.D. student only as last resort.