Is it possible to attend school 1/2 day and homeschool 1/2 day in your school district? (it is in ours - it isn't exactly advertised, so most people don't realize it's an option, but it can happen). My first thought when you asked about an online program that can switch between Spanish and English is - why not just let her enroll in an online Spanish course? I realize the one trade-off is lack of exposure to English, but if the child also attended public school for 1/2 day during PE/Music/etc and studied 1-3 core classes at home at her own pace, in Spanish - the child has intellectual challenge, the mom can be involved in the study, and the student also has the chance to be with other kids as well as practice immersive English for part of each day.
I wish there was half time homeschooling!! I would jump at the chance for my kids!! Interesting thought about homeschooling. I know of many many resources here to support homeschooling families. What I don't know is if any of the families speak Spanish (although some of the groups are very diverse they generally are not composed of families which speak Spanish).
Even if she chooses full home-schooling, I'd still consider enrolling her in some of her courses in Spanish so the mom doesn't have to focus on translating but instead can just enjoy being able to help with her daughter's studies.
I will mention this. The mom can keep an eye on how she is doing plus she will strengthen her skills in Spanish (that's an issue in itself - many of my clients speak another language but do not learn how to read or write in that language).
The other thing I'm wondering - is their a gifted program available in the public school for her grade? If so, you should be able to request testing that is intended not to be biased against non-native English speakers (if you are concerned she wouldn't test to her full ability on a test administered in English based on growing up in a bilingual household).
No gifted services until 3rd grade. Even after being identified kids get about an hour per week with the gifted teacher unless the school adds a bit more because they feel strongly about this.