I have three kids, and we never made them sit on the potty. A 3 1/2
year old is smart. You pick a date, circle it on the calendar, buy
them new underwear, and go cold turkey. They will figure it out. You
don't need to schedule potty sessions (total waste of time and way
more time and effort than this mom had patience for). Expect a fair
bit of laundry, but the very vast majority of kids your daughter's age
will "get" it within a few days.

That is not to say they will be dry at night, as that is a whole other
thing (its a function of physiological maturity and often takes much
longer than daytime dryness).

I would not let my kid be left behind in school or left out of
activities and play opportunities because of toileting issues. I think
you are confusing readiness and desire. There are lots of things kids
are quite capable of doing but don't necessarily WANT to do, including
picking up toys. Sometimes some low level parental direction is not
only needed, but a Good Thing for everyone in the bigger picture.

Mary G.