I'm a licensed nail technician, maybe I can help.
First - fingernail issues are very similar to hair - they can show a lot about your body. You want to be sure that she is getting adequate nutrition - well balanced meals, and not a lot of junk. Not saying that she's not, but, diet is a huge factor in the health of your nails and hair and this should be addressed first before additional chemicals added for change.
Second - Polish always breaks down your nails, especially if you're not using a base coat. It is a chemical, and therefore will have affects. Nail brand polishes, however, will do this less often as they are better quality. I prefer Creative Nail.
Third - When your nails are too moisturized, they often peel. Depending on the brand of your polish, this can affect the nails more and cause this. Higher quality brands, like Creative, do not do this as bad, but, you still need to use a base coat to further protect the nail. Be careful with strengtheners as many of these contain formaldehyde - make sure you're getting one w/o this in it. It's not healthy for an adult, let alone a child. Too much strengthener will cause them to become brittle, however (as will them being too dry).
Fourth - Be sure before applying any polish that the nail is well manicured. Push the cuticles back gently - and if you're cutting any cuticle away, it should only be the dead loose cuticle from the nail bed. Completely clean and dry the nail plate before applying any polish... You can do this with rubbing alcohol. Apply a base coat, to enamel coats, and one top coat. Let these dry in between, and dry for at least 60 seconds after the last coat. Then apply a cuticle oil - this can be as simple as Olive Oil or Vegitable Oil.
Check this out if you're interested in more information:
http://healthynails.onlineclasses.com