Wow, "force" is such a powerfully negative word, and if that's what you end up doing, in practice or in spirit, it's not too likely to bear positive fruit.
I was also an underachiever in school. Homework was for the most part repetitive busywork, and deadly boring. My resentment toward my over-controlling mother was probably part of my problem; hard as she tried, she could not *make* me do my homework, though there was much grief in our household over my "laziness." I know she earnestly wanted me to "fit in," but I wasn't lazy, I was other-directed, and as I look back now, pretty smart for not wasting my valuable life on unnecessary effort. (I also have learned, much after the fact, that I was/am ADHD.)
Why would I want to drill on math or grammar or history facts that I already knew, when I could be investing that time in independent studies into geography (through stamp collecting and map reading), biology (through raising tropical fish and gardening), astronomy (I read every book in the library), geology/minerology (through rock collecting and much more reading), or art (I am today a graphic designer and illustrator, and I also edit a series of hands-on science books that my husband writes). I also started reading philosophy at an early age. Now that homeschooling is such a popular idea, I recognize that I largely homeschooled myself.
I have this anguished (because it's probably out of reach) longing for schools to recognize that homework is not good or necessary for all students. I could have gotten straight A's if not for homework that I didn't turn in. I was usually able to ace tests and give the right answer if called on in class, but the "rules" dictated that cookie-cutter repetition would somehow make me a better person. Ugh – so many of my school memories are tainted by everyone's dissapointment and pressure.
If your daughter is bright and lively, why not leave her educational achievements up to her? I did this (to some extent) with my daughter, and she got from her education what she needed, went on to get the secondary education that would help her achieve her goals, and is highly successful today.
Or, here's an even less conventional idea: if she's doing reasonably well in school, why not intervene on her behalf with her teacher(s)? Ask whether she can be allowed to cut back on at least the busywork assignments if she participates in class and makes passing grades on tests. Perhaps she could choose some extra-credit projects to demonstrate her interest in areas that excite her. (A caveat: Teachers today are overburdened as it is, and asking for special consideration may get you tagged as a problem parent.)
I'd like to add that I have very little college in my resume, and yet have creative, demanding work that I love and that suits me perfectly. I have multiple acquaintances in similar situations. So if your concern is that your daughter will not qualify for a top-ranked college, keep in mind that there are millions of successful and happy people who have taken alternative routes to realizing their potential.
Good luck. I'm sure you're proud of your daughter just for being who she is. I hope you'll be able to support her uniqueness!