Old chair with orange dust  

It is polyurethane dust, from the polyurethane foam breaking down.

As with any dust, if you inhale a certain amount of it, it can be bad for you. That being said, a sand box has silica dust in it, and if you breathe enough of that in it is bad for you. What is that threshold? .... you would have to consult an expert for an accurate answer to that question.

I am not a toxicologist, but I have a hard time believing that the offending chair is producing enough polyurethane dust to expose your toddler to the specific threshold that is detrimental. The good thing is, if your chair was produced prior to 1975, that there are not likely any flame retardants in that foam dust. Those should be the primary exposure concern for a developing child. I think you will get many more safety miles out of limiting your child's exposure to endocrine disruptors in plastics, and other developmentally damaging chemicals , than worrying about some PU dust from a vintage chair.

I suggest you do your aunt/cousin a solid, and get the chair refoamed. Problem solved.

Or it's latex foam that has hardened and crumbled into dust. That stuff can be so fine that it can sift through fabric. I don't know if it has any dangerous chemical properties but it could definitely be an irritant if you inhale enough of it.

The deteriorated urethane foam crumbs that I've seen have been more on the gummy, sticky side than dry like sawdust. But both are messy and not something you want to have around the house.

Well,

Look at what the orange dust did for Donald Trump!

Impressive,

Aunt Mark