I went to art school "many moons ago" as well (and have CF). I'm surprised your sister would suggest that acrylic paint might be harmful. Of course, anything could cause problems for people with unusual sensitivities, but in my experience acrylic paint has no discernible smell and is not considered to have harmful fumes. There are pigments used in some colors that are toxic to ingest (e.g. cadmium orange/yellow/red -- look for warning labels), but those are easily avoidable these days. I wouldn't hesitate to give your daughter acrylic paints. If you would like specific brand suggestions, both Liquitex, Winsor & Newton, and Golden acrylics are high quality and readily available.
You didn't ask about oil painting, but an FYI for those who might be interested: There is nothing inherently harmful about oil paints, either. Artists' oil paints are simply pigment in linseed oil. While linseed oil has an odor that some may find unpleasant, it's really the solvents that can be problematic. Turpentine was the traditional solvent and should definitely be avoided. More common today is odorless mineral spirits, which is not as bad, but requires good ventilation. The good news is that it is possible to avoid all solvents. You can use regular vegetable oil to get paint out of a brush, wipe the brush on a paper towel, then wash with soap and water. Several companies make solvent-free painting mediums (gel or liquid you mix with the paint to change its consistency). Another option is "water mixable" oil paint, which I have not personally tried.
As with acrylic paint, toxic pigments are sometimes used -- in fact, they are probably more common in oil paint, especially the higher-end brands. This includes lead white colors like Flake White and Cremnitz White! But rest assured there are always non-toxic substitutes and the toxic paints will always be marked (and more expensive!). I seriously doubt any prepackaged set of paints would included toxic pigments.