In Alberta, an employer is allowed to lay people off temporarily if they do not need their services. If they were to go by the book, they would let you know in writing. I do not think they can use your overtime to cover the day off unless you have an agreement with them to bank your overtime. Banked overtime means that you do not get your overtime paid out, they however keep a note of how many hours they owe you and try to give you time off instead.
If you are banking overtime, the law states that if they are unable to give you time off for the overtime within 3 months of it being worked, they must pay it out at 1.5 times your regular hourly rate.
If you have no agreement with them to bank your overtime, they should pay you for your overtime at 1.5 times your hourly rate each pay period but if your services are not needed and you have an extra day off, you would not be paid for that day.
You can look for the rules on temporary layoff here: http://www.employment.alberta.ca/documents/Termination-of-Employment-and-Temp-Layoff.pdf and overtime hours here: http://www.employment.alberta.ca/documents/Overtime-Hours-and-Overtime-Pay.pdf Special rules may apply for live-in caregivers. There is a phone number at the top there you can call if you are not sure about something.