First thing I want to say is to "Do it!", second thing I want to say is that there's some really bad smelling comments in this thread already.
Some facts. You're thinking of visiting the Nordschleife Nürburgring, not the Grand Prix Nürburgring, on a Touristenfahrten. That is "tourist drives". During these times the track is open to the general public on the same premises that a normal German road is open; you have to have license, your vehicle has to be in road going condition (i.e insurance, tax, M.O.T) with a few addendums. You must be able to travel faster than 70km/h (i.e no tractors) and so forth. You may
not use race tyres (slicks etc), loud exhausts, cars without brake lights, etc.
Above all,
all German road rules apply. That includes to drive on the right and pass on the left (very important rule!!). If you have an accident, German law applies; Police will be called, insurances will be put into play, and if you've been an idiot, you'll face fines, prosecution etc.
This leads to another very very important point;
It is NOT a race track.
Racing during Touristenfahrten is not allowed; Verboten!
Some trivia; It takes between 50 and 100 laps, at 13 miles a pop, to learn
where the track goes. It takes a lifetime to master it. In short; don't even think you know the track. Don't drive fast because you think it's a race track, only drive what you can see when you're a newbie.
How do Touristenfahrten accidents happen? Two things:
1) Driver/Rider goes over his/her limits. Doesn't know the track, can't drive/ride the vehicle. Red mist. Racing. Etc... You
can affect this; Don't overdo it.
2) You have "someone elses accident"; Oil spills/coolant spills. They're just on track and you can't avoid them. Another thing is you come around a corner and there's a car that's spun or a bike that's down and you need to avoid it. These things you can't control in any other way than make sure that you can stop your vehicle safely. Just like on the road (remember the part about this being a road)!
Customs on the track.
It's customary to drive on the right, and indicate right to let someone pass. If you need to pass, you make sure you don't have a faster car passing you, and then indicate left, and pass on the left. Let traffic take the corners alone, try to overtake going out of corners or before going into corners. Exception is obviously when a slower vehicle goes way offline in a corner to let traffic past.
Check your mirrors; Before the corner, in the corner, after the corner and at the middle of the straight.
Bikes are different to cars. Bikes accelerate better than cars, but corner and brake worse. This means that a bike will overtake your easily out of the corner, but might be holding you up going into a corner or around the corner. Bikes also have more issues altering the line through a corner once committed to a line through a corner. Also keep in mind that a bike gets "wider" as it corners and leans over.
If you have issues with bikes (or cars for that matter), just drop back for a while and let the traffic clear. You have around 10 minutes of fun per lap. Don't spoil it by red-misting in traffic when you can "waste" 30 seconds to drop back a bit to some clear space.
Bikers thank you by lifting their foot off the peg; it's not a threat or angry gesture.
Remember; you all have equal rights to be on the track, regardless of vehicle type and/or make/brand/model.
A good tip is to get yourself a "hare", i.e another person that can drive in front of you that knows the track. This person can keep an eye out in the mirrors so you can spend a little more time focusing on going forward. If the car in front of you indicates right and goes off-line you'll know there's faster traffic approaching from the rear. They can aslo pace you to make sure that you don't overcook Adenauer Forst for example.
If you want to do it slightly more serious; rent a car from RSR Nürburg, and/or an instructor. Many of them are good friends of mine and are top notch blokes, on or off the track.
With regards to taking your family and children onto the track, it's largely up to you and how fast you're going to go. First get a passenger lap or three with someone else. Then I think that you should consider going out on your own with someone experienced in the passenger seat to guide you around to get a taster, and then take your family out. Put into perspective, there's constantly coaches (yes, big buses) and campervans going round at an incredibly sedate pace (to the right with right indicator on). I have not witnessed any of them having accidents.
Note that there's always some jerk somewhere that'll only think of themselves and spoil the fun for others. Just don't let them get to you, simply stay away. There are incredibly fast cars and bikes out there, but they tend to be very seasoned and they know the "code".
Lap tickets cost what they cost, there's no discounts etc. You might find cheaper ones on eBay from people who've gone over and not been able to use all laps. Buyer beware though as you can't check how many laps the ticket has got.
There are fatal accidents, but sometimes it's very juicy to speculate in them. Nürburgring GmBH does not release any figures so, it's speculations.
Bikers don't stick their heads through windows of cars. And so forth.
With regards to spectating and the area in general. Nürburg, Adenau and surrounding area is a haven for motor enthusiasts. Imagine a place where you don't have to be ashamed of having petrol flowing in your veins! There's tons of cars and bikes to look at. There's several good spots to spectate and take pictures. All in all, a wonderful atmosphere situated in an incredible surrounding.
Think of the Nordschleife as a wonderful one-way B-road and you should be able to have a great experience. And the "code" states that once your car has been around the track, it's allowed to wear a Ring-sticker.
Please ask questions if you have any!
He was banned this week, for alledgedly "taking taxi passengers". Back on track now. 
