Schedule on Tuesday
Solution 1:
I would take the sentence to mean they want your appointment to be on Tuesday. The following sentences would remedy the ambiguity:
On Tuesday, we want to schedule your next appointment.
Your next appointment is Tuesday.
Solution 2:
"We want to schedule your appointment on Tuesday" means the scheduling will take place on Tuesday rather than the actual event itself.
"We want to schedule your appointment for Tuesday" would indicate that the event will take place on Tuesday.