Is there a way to use the Galaxy Tab 2 with my Galaxy S3 (SPRINT) to get an internet connection?
Yes, very easily actually.
To Make your S3 emit a WiFi network
To Connect your Tablet to the WiFi network
If you do not see the WiFi Hotspot option, then your network has disabled it. If you're rooted you could use an app such as WiFi Tethering - just be aware that this will produce an Ad-Hoc hotspot, and Stock Android cannot connect to these types of hostspots.
There is currently no way, AFAIK, to create a standard WiFi hotspot without using the stock android tethering system.
I assume that you have
On Galaxy S3:
Now, on your Galaxy Tab 2:
What I did is to root my Samsung S3 and install a WiFi Tether apk file so I can get free internet on my Samsung Tab 2.