Yes, your DD can get CP from your mom's case of shingles if she comes in contact with the open sores. She likely will not get it just from being around (but not touching) your mother.
My DS is almost 3 as well and if I had the opportunity to expose him and get a batural infection, I would. I work full time outside of the home and would have to miss quite a bit of work, and Id still do it.
If my DS had CP, Id be calling our ND who has a variety of homepathic remedies to aid the body in recovering from this illness.
As for your mom tell her to take Lysine. Lysine prevents the absorption of arginine which the shingles virus needs to stay active. Take 1,000mg of lysine up to three times a day.
Use Apple cider vinegar to relieve pain. You can apply the acv directly on the affected areas by dabbing it on with a soft cloth. Let it dry and then repeat as often as needed. It helps the blisters heal more rapidly.
Id also tell her to take vitamin c to bowel tolerance to suppport overall immunity. I would tell her (this goes for your DD too if she gets CP) to avoid reducing the fever with tylenol or advil. This can cause complications. There are homeopathic and natural ways to reduce fever for comfort if need be.