DSLR vs point and shoot vs mirrorless?

Background - I have limited photography skill, used to shoot with a film SLR, have owned and wrecked 3 Canon point and shoots in 4 years, all with the same lens jam. Now I need a new camera to shoot pics of my kiddos.

My latest Canon was an Elph and SUPER portable. I would say that I loved it but for the spontaneous lens jam (the other two Canon jams were my fault as I dropped the camera both times).It's as expensive to fix it as it is to buy a new model exactly the same, so I'm looking at possibly getting something different. Friends tell me of lens jams in their Nikons, Sonys, and Panasonics, so I know though particularly problematic in Canons, switching brand won't solve my problem.

Has anyone made the switch to DSLR? I'm not concerned about being able to work the controls, more about the portability. I love taking my camera everywhere, and loved the pocket sized Elph. I'm also looking into mirrorless digitals, which seem to be a bit of a compromise and a way to avoid the lens jam issue that seems to be plaguing me. Does anyone use a mirrorless? I'm looking at the Olympus PEN E-PM1, the Nikon J1, or the Panasonic GF3.

Any experience or recommendations on brand, etc. Would be much appreciated. Thanks!

Added (1). EDIT:
Lens jams in point and shoot models only. Update though, I was trying to fix the latest lens jam and dropped the camera and it works again! I think I'll start saving for an EVIL now, as it's sure to happen again soon.

Mirror less are better than point and shoots as they are more versital. They are much more portable than a dslr and easier to use. I'd go with one of them for what you described.

A P&S camera has a sensor that is about 15 times smaller than a dSLR (Nikon, Canon, Pentax, Sony)

The Olympus and Panasonic cameras (4/3rds) cameras have sensors that are roughly 9 times larger than a P&S camera.

As you can see, the sensor sizes are different from a standard P&S camera.

What is also something for you to consider is that cameras that are fully adjustable, like dSLR's, EVIL and others have many choices when it comes to the lenses you can buy for them.

Where on earth you got the idea that lenses jam with Nikon and Canon's I don't know? If that were true, professionals could not depend upon them and would be looking for other camera systems.

I personally have Nikkor lenses that were made in the early 1970's which still work perfectly with my current dSLR cameras and I have four AF-S lenses purchased in 2002 that are still auto-focusing perfectly and quickly while shooting assignments from shooting professional sports, for magazines and shooting products in the studio.

If you are looking for a camera you can put in your purse or brief case that uses interchangeable lenses, the Nikon 1 series cameras my be a good choice. It is a new form factor, but I'm getting good feedback from my colleagues who purchased them for shooting their "personal" photography and some video from time to time.