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1)The jewels are not in the car.

Should one say "The jewels are OUT OF the car." or "The jewels are OUTSIDE the car."?
(They have not be carried out right now and we are not sure that they are near the house.)

2)The jewels are not in the country.

Should one say "The jewels are OUT OF the country." or "The jewels are OUTSIDE the country."?
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I would say "outside" or "outside of" in both cases.
Comments  
The opposite of in(to) is out (of).

He is not in the office. > He is out of the office.