If calorie burning is your goal, you are certainly correct -- jumping on a mini-trampouline does not have the same calorie burn as activities that have impact.
That said, trampouline would be an excellent activity on your "rest" days. Also trampouline is a great way to warm up. Have you seen the use of the trampouline for a "non-stable" surface for enhancing balance and core work as part of strength training?
Do you have a regular pattern of exercise already established? Sometimes what you feel good about doing, that gets done, is more important than Activity A, which is done inconsistently due to injury or lack of buy-in.
Best wishes in finding the combination of exercise that lets you reach your goals. www.sparkpeople.com/resource/fitness_artic
This article, 8 Cold, Hard Truths about Exercise by Coach Nicoll, may give you some ideas on choosing the activity (activities) that will meet your needs.