The one piece of advice I heard that has stuck with me is that parents in other cultures hear "math is hard" too -- they just don't accept that as an excuse to stop doing it. Of course math is hard, particularly when you get to more abstract ideas like algebra, which are well beyond what most kids have been asked to do at that age in any other class. But that just means you have to study it more until you get it.
I agree that giving her more insight into the possible long-term career paths is a great idea. We have always told our kids, since they were little, that they can follow any career they want, as long as they are willing to accept the tradeoffs that go with it. So if they have a passion for art, then that's great. But they then need to know what the possible career paths are and make sure to get whatever other skills are needed for those paths (business/marketing/computer skills/etc.) -- and be willing to live on that salary.
I would also suggest that you help her develop other interests besides art, because art is something you can do as a hobby, while it's harder to do science that way. And it is completely appropriate for you to lay down the law about your own minimum requirements, regardless of what the schools say. IMO that is far too early for a kid to limit herself, unless it is a passion and talent that the kid has spent a lot of time focusing on for years. So stop focusing on the HS choice now, and start nudging her to explore other things as well -- other careers she might be interested in, other interests in school. Start talking to people who went all of the different schools and see what their university options were, what careers they were able to build from them, etc. Personally, I would have no problem with an art-focused school, if it also provided a great education in other areas. But it would be reasonable for you to insist that any HS option had to meet minimum criteria for quality education in a number of areas -- and if any of the schools don't pass that threshold, they're off the list. (Or, you know, tell her she can go to the art school, as long as she's willing to spend extra time at home meeting your math/science criteria. ;-))
Finally, please don't be fixated on the math/science school. Engineering is a great, practical career, but it is not the be-all, end-all, and is definitely not suited to everyone (speaking as someone who just went through this argument with her engineer-husband over her own daughter's college choice). IME kids do better if they get to do something that interests them, vs. being forced into a particular path by a parent. IOW, I think it's ok to veto any of the highly-focused schools if the "other" areas aren't up to par, but don't force a particular choice otherwise.