Yes and no, depending on one's definition of gluten.
I don't have all the proper references on hand right now, so please forgive me if the explanation is missing the full chemical explanation (references to peptides and such). I'm recalling all of this from memory from a presentation given by an all-types-of-gluten celiac I met several years ago.
All grains contain "gluten," but there is more than one type of gluten. When one commonly refers to a gluten, that person is referring to the type of gluten found in wheat, barley, and rye. (Oats are often in contact with wheat. As a result, oats may contain enough gluten to set off a celiac and are often included on the list of banned grains.) Rice contains its own "glue-like" properties and proteins, but it is not the same as in wheat, barely, or rye. Rice can contain both starch and protein, same as wheat. 'Glutinous' refers to starch, not protein.
So your sister-in-law is safe to eat rice, so long as she only reacts to the generic "gluten." In which case, tell her to watch out for soy sauce, as that often has added wheat.
The OP mentioned that his sister-in-law's health improved by removing certain foods, such as gluten. The gluten she needs to avoid depends on her level and type of intolerance. In rare occasions, one will not have a textbook case of gluten-intolerance or celiac. My sister is a textbook celiac; I have a nonstandard gluten-intolerance. She can eat rice; I cannot. In short, if the gluten sensitivity is standard, consider all rice to be gluten-free. 'Glutinous' merely describes the amount of sticky starch in the grain (and possibly its fattening potential ;) ), not gluten.