I'm living in Karlsruhe since mid-2009 and work as IT Sysadmin. I currently make around 50k/year and can live extremely well from this. (I'm not married, no kids, tax class 1.)
As other people wrote your salary should be fine for living in Karlsruhe/Germany. If you own a car and don't mind commuting to work every day you can pick a nice flat in some of the towns around Karlsruhe which don't have a good public transport connection (or none at all).
Rents there are usually lower as they are not that preferred from students and people without a car, so the competition for these flats is usually smaller.
If you want a nice flat in the city you should take your time as flats for a family with 2 kids can sometimes be hard to find on the market.

Overall Karlsruhe is very safe. Yes, you have the occasional burglary or stolen car. Some fist fights. But: I only ever read about it in the newspaper. I never witnessed it myself. 1 of my colleagues was victim of a burglary years ago, but that's it. And.. These are things you have in any city world-wide.
There, for example, are no "No-Go areas" or areas "Where you shouldn't be at night" it's rather the question of "Do you feel safe?" than "Are you safe?".