Gas Gage

I know nothing about cars so i have a question. I posted about buying a Chevy Tahoe a few days ago, which I did buy, and am having a problem already and it is in the shop right now.
When I drive it says that the gas tank is full and all of a sudden drops down to E while driving and then goes back up. It kept doing this.
I had my 3 kids in the car and it dropped down to E and ran out of gas right on the highway with a semi behind us! I freaked out. Finally after help, I put just 3 gallons in to get to the gas station and it went up to full!
The shop just said that they are replacing the fuel pump. Does this sound right? I kinda need to know how much gas I have especially with 3 kids....
anyone have any ideas?

It's not the fuel pump, it's the float (although it is mounted to the same carrier the fuel pump is). The sending unit a fuel pump is not.