Kindy is usually from 3-5yrs, but some will let kids start a little earlier if they are toilet trained.
If u want both kids to attend the same place, you could look into an early chilhood eaducation centre/ childcare centre/daycare. Some will offer the government subsidised 20 free hrs per week for over 3's, and some u will need to pay a bit extra. You will need to pay for your 2 yr old. The prices vary greatly from area to area. And Im not sure if u will be entitled to the subsidy since u are not resident here anyway.
Normally you would either ph up or go into a centre to enquire. You wont need to apply in writing, but will need to complete an enrolment form. Again it depends on the invidiual place, and the area your in as to the length of waiting lists.
This link might be a good starting point!
Dunedin Kindy association
Check out this thread for other mums in your area too
Dunedin meetups
Edited by Kellz