Lavender is one of the safest oils used, and your daughter's issue is the first I've heard of Lavender causing any skin issues.
Aromatherapist Shirley Price suggests that only a small number of people (0.1%) have a skin redness reaction to appropriately diluted essential oils. Skin receptors can become sensitive . . . which not necessarily an "allergic" response. I would not continue to apply it though (this is known as 'hapten').
I'd think you could diffuse the Lavender without any problems, but again, this is new territory for me since I have rarely heard of anyone having a true "allergic" reaction to any essential oil. For example, if I put Cinnamon essential oil on my arm, it will redden and feel hot and uncomfortable. I don't consider this an allergic reaction, but rather too hot for my skin. I'd need to dilute it quite a bit if I needed it on my skin, but I could diffuse it without harm.
I hope we hear some feedback from others. Keep us updated.
Blessings and prayers for wisdom,
Linda