At one end is ASL, which its own language as you said, although with some influence from English).
On the opposite end are things like Signed Exact English that reproduce English verbatim on the hands, borrowing from ASL in some places and inventing signs in other places. For example, ASL has no sign for -ed (the past tense ending) because it marks aspect instead of tense, so SEE invented a sign for it.
And in the middle is Contact Sign or Pidgin Signed English, a sort of compromise between ASL and English grammar, which is most used when ASL speakers and non-fluent speakers communicate. You might get a mix of some ASL topic-comment word order with some English subject-verb-object word order. You'l get a lot less "simultaneous" ASL grammar like indicating the subject or object pronoun using eye gaze, or conjugating verbs by changing motion, because those are hard for non-fluent ASL speakers to understand. You'll also get a lot less of the SEE constructs like explicit -ed markings, because they're usually obvious from context.
Not a huge shock, since you also get this between two sole English speakers communicating vocally.
The romance languages were taught in English, with a strong focus on the rules. Progress was extremely slow. I've had opportunities to practice Spanish and Italian, and that's been way more helpful than those classes ever were (and let's be honest, Spanish and Italian are too similar for my muddled brain and "communication" is more of a negotiation). I've heard from quite a few students of French that after 4 years of formal study, they can't speak a lick. I didn't hang on that long.
ASL is often taught immersively. You might have an interpreter for the first day or the first week, but after that, it's voices off (and if you're lucky, your instructor is Deaf). You start with letters, to bootstrap from English, and mimeing, because that forms a basis for a lot of informal ASL. Subsequent vocabulary is communicated through a combination of fingerspelling and mime. Grammar is considered a fairly advanced topic; and by the time your teacher gets around to that, you'll have absorbed more of it than you realize.
In my experience, learning ASL is more akin to riding a bike, than learning a romance language -- much less Chinese.
The fact that you had formal language classes in romance languages doesn't mean that's the only way romance languages can be taught or learned. You can learn or teach any language however you want. Some ways are more effective; some are less effective.
One reason students can't speak any French after taking four years of school French is that effectiveness isn't really a goal of the instruction (or of the students).
Fortunately the effort can be done anytime after the fact, so if she is lucky it might not be done at all.