Rear rattle when driving over bumps, it stops if I'm applying the brakes - HELP!

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I have a 2006 Mazda 5. Over the last year I've noticed some rattle sounds coming from under the car. The mechanic looked at it and said that there were a lot of rocks he took out of the undercarriage (a few times a year we drive down logging roads to visit family). Anyway, that clearly was not the problem. It started as an occassional rattle when going over bumps but it has progressed to the point that simply driving anywhere causes it to rattle (rear driver side). The funny thing is....I've noticed that if I'm applying the brake, the rattling stops. Is this a brake issue (or related brake parts) or does it sound like a sway bar/bushings or a loose stabilizer bar link (sway bar end link) that other owners have commented on? The mechanic my husband goes to doesn't seem to know what's going on. I would like to get some insight from someone so I can at least point them in the right direction. It's completely annoying to drive around in a car that looks great, but sounds like it's going to fall apart at any moment. If this situation is brake related and potentially harmful to me or my family, I would like to get it fixed ASAP. Thank you for reading!