You will need to first adapt your Mac Mini's DVI output to vga using a simple adapter like this:
Or you can pay twice as much for the official Apple branded one:
This will adapt it to run your touchscreen. To get the video screens going you'll need a VGA to TV converter like this:
This will convert VGA to composite or s-video for your video screens. It also has a pass-thru vga port to plug in your vga touchscreen. You will need to "split" the composite output with a y-cable to send the signal to 2 screens:
Alternatively you could run S-video to 1 screen and composite to the other, or split the s-video and run that to both - whatever works.
So the "chain" of adapters will be
1. DVI to VGA adapter
2. VGA to TV converter
3. Composite out of the "VGA to TV converter" gets split and sent to both video screens
4. VGA "pass-thru" is sent to vga touchscreen.