Since she did open the house for you on two occasions, there's an assumption that's she's working for you. Now, that doesn't mean you're legally obligated to go through her, but if you write an offer with another agent, she may complain and cite "procurring cause", which means she's the first agent who showed you the house and therefore she's the one who has the right to represent you in its purchase. That would, however, be something that the two agents could fight over -- you could still buy the house with another agent and let the chips fall where they may between the two agents.
You may also consider calling her broker and explaining the situation. This would likely snap her to attention and the broker would probably help guide her in pulling comparable sales data so you would have the information you need to make an informed offer. This, of course, may not win you any points with your future neighbor either, but it's another option.
A third option would be to simply tell the agent that you're considering making an offer but that you don't want to unless you've seen some comps for the house. If you give her one last opportunity to do her job properly, she may surprise you and be more helpful. She may not do what you ask, but at that point, you could ask another agent to write the offer with a clear conscience since you've given her every chance to do her job.
Keep in mind it's conceivable that there really aren't any "true" comps for that property -- if nothing else similar to it has sold within a mile of that property in the past year, she may actually be telling the truth about the lack of comps. This will make the appraiser's job more difficult and (just to give you a heads up) could result in the house not appraising for the purchase price. This has become more of an issue these days with restrictions having become so tight on which properties appraisers can use as comparables.
I guess the question you have to answer is: based on your own assessment of the property's value, do you feel that you have enough information to make an informed offer? If so, in the interest of keeping the peace, you may want to let this woman write the offer. But if you really want to work with someone who's going to guide you in a professional manner, by all means feel free to find someone else whom you believe WILL work hard to represent your best interests. Good luck!