I guess that begs a few more questions, but for right now...
There is no specific book on sign making for a cutter and printer.
There are books that touch on it. Most information is in magazines and taught on the job.
If it were me, I would get subscriptions to:
Signcraft Magazine
Signs of the Times
Sign Business
The books I have are:
"Getting Started in the Sign Business" - The Editors of Signs of the Times (Basic Sign Business)
"Mastering Layout: On the Art of Eye Appeal" by Mike Stevens (Layout of signs)
"Vinyl Sign Techniques" by Jim Hingst (Slightly dated, good information of vinyl signs)
If my kid (I have 4 boys by the way) was interested in signs. I would train them the second they showed interest. Probably in design first... while they swept the floors, weeded some vinyl, and took out the trash. The only sign book I would have them read is Mastering Layout (at first), after that, any design book that put an emphasis on the design process and practicing the idea of conceptual thinking because the mechanics will come later.
I have quite a few books, ones I think are fun to look at and might widen out her skills (and your shops) are about graphic design, which is applicable to sign design:
Logo Design:
LogoLounge Series Volumes 1-5
LogoLounge Master Library Volume 1 (Volume 2 coming out soon)
Logo Design for Small Business
Logo Design for Small Business 2
Design Matters: Logos 01: An Essential Primer for Today's Competitive Market (v. 1)
Logo Design Workbook: A Hands-On Guide to Creating Logos
Letterhead and Logo Design 9
Letterhead and Logo Design 10
Letterhead and Logo Design 11
Logo Lab
The Secret Life of Logos: Behind the Design of 80 Great Logos
Type:
Thinking with Type: A Critical Guide for Designers, Writers, Editors, & Students
1,000 Type Treatments: From Script to Serif, Letterforms Used to Perfection
Retro:
New Vintage Type: Classic Fonts for the Digital Age
Hatch Show Print: The History of a Great American Poster Shop
Posters for the People: The Art of the WPA
Logo, Font & Lettering Bible
Euro Deco: Graphic Design Between the Wars
House Industries 10th Anniversary Book <---- Highly recommended, hard to find now
Then is Now: Sampling from the Past for Today's Graphics
Retro Graphics: A Visual Sourcebook to 100 Years of Graphic Design
Retro Style Graphics
Graphically Speaking: A Visual Lexicon... <---- Highly recommended
Tinspiration: The Art and Inspiration of the Fossil Tin
Design and designey books I dig:
The pixar movie books.
Walt Disney Imagineering: A Behind the Dreams Look at Making the Magic Real
Modern Dog: 20 Years of Poster Art
Gig Posters Volume 1: Rock Show Art of the 21st Century
Art of Modern Rock: The Poster Explosion
The 1000 Series collection... elements, type, retail, packaging, Music graphics, Greetings, bags tags and labels, restaurants are good.
OBEY: Supply & Demand - The Art of Shepard Fairey
Chromaphile
Vernaculis
Symptomatica
Got Your Nose
Izzy's Very Important Job
Big City
Kings Of The Road