I've done edits for FCs before but as Ryuko mentioned I've always vectored the image myself based off the crest.
If you go this route- ask your daughter if her FC has a house or if she has a private house in game. If they do and they have a company chest inside of it then you can get a slightly larger picture to use for your vector. (You'll still have to do some work to it but at least it will be easier to trace/vector youself)
Quick example screenshot I pulled from my Alts FC.
Also, depending on what rank your daughter is in the FC she may be able to access the crest edit system (if she doesn't maybe she could ask an FC leader for temporary access? (The NPC location will depend on which city-state her FC is affiliated with so keep that in mind it may be slightly different NPC look from this shot)
Also, I've done some embroidery myself with this game's logo/graphics- where you planning on running them on a twill base then using the stiches for the 3 parts of the emblem? Or which parts were you considering being stitched just the top 2 layers aka 'Charge' and 'Ordinary' or where you looking to include the 'Escutcheon' as well.
Example: What you described for your daughters FC was:
Charge- Goobue
Escutcheon- ???
Ordinary- two-color Spiral
Whats the Escutcheon of your daughters FC's crest? (for example the above image my FCs Escutcheon is a heart, with a flat color for the Ordinary, and a diamond for the Charge)