brantly, for what it’s worth, I have no problem with being an English major, but those jobs for English majors tend to require specific locations. My sil ended up in NH with an English degree from Harvard - where opportunities for jobs for her skill set were pretty slim.
All that said, I think 14 is far too young to be worried about college majors, but not so young that you should cut yourself off. My math kid took 4 science classes and 3 AP science classes. (One hs level science was offered in 8th grade and one he took in the summer to avoid some scheduling issues, he took an extra science as a senior as an elective. My non science kid took 3 science classes, plus 2 AP science classes.
As for how to work out the two cultures I think the OP is already doing a pretty good job. At this point you don’t want to cut off options. So I would suggest that the OP’s daughter take science and math every year at her level of ability. Then apply to appropriate programs/colleges when she is a senior. If at that point engineering or comp sci look attractive, some colleges will want her to declare her major, others won’t. That said, some (especially engineering type) majors will be hard hard to complete in four years if you don’t take the right courses as a freshman.