Asbestos fibres "live" as long as they are around. That is to say the dust settles in nooks and crannies and are most partial to air ducts. If you feel unsafe, you can have someone take some swabs/samples from areas of your house and send them off for testing (about $100/sample). If they find anything then you can decide whether or not you wish to do anything about it.

Testing first, decision later. And then you can find out if the person(s) responsible for the renovation owe you/your family any form of financial compensation for lack of proper disposal/remediation. A lawyer familiar with building law will help with this...if it becomes a concern.

The amounts should be minute. Of course that doesn't make you feel any better...but it should be pretty small. Today's flooring installers are showing very few signs of asbestos related illnesses and they are being exposed (unknowingly and knowingly) on a daily basis with amounts that would be a few times higher then what your family has experienced.

If you feel the need to be SUPER cautious, you can look at having chest X-rays done every 5-10 years...but the exposure to X-rays will possibly be worse than the exposure to the minute amount of asbestos in the air. This is when the cure is worse than the disease.

It can take decades before mesothelioma will develop which makes it harder to pin to one single cause. Here's a nice link explaining the levels/types of exposures:

http://www.cancer.org/cancer/cancercauses/othercarcinogens/intheworkplace/asbestos