Setting up 2 external monitors on a laptop with VGA splitter

1.Can I just use a VGA splitter?

No.

A splitter just 'splits' the same image. You can use them to get two identical displays. But your premise was unique displays. That is something you can not do with a splitter.

2.Would it a VGA to 2 DVI splitter give a better picture quality?

Also no.

DVI comes in several flavours. Most of them just carry a digital signal and some of also carry the analog signal. If you have an analog (VGA) out and use a DVI slitter you get the same picture quality. (Or worse if some is lost in the splitter).

The better picture quality attributed to DVI is from the digital signal which works even on relative cheap or poor quality cables. Using VGA, cheap cables and high resolution often results in ghosting. (Which is one of the reasons DVI is often better at decent resolutions. Even though proper cabling can solve that).

3.Would I be better upgrading laptop to one with 2 digital ports ( I just see a lot with VGA and HDMI though)

There are several ways to get a decent independent pictures:

  1. Upgrading the laptop is one of them.
  2. Getting a docking station with more outputs is another.
  3. For slow displays which do not require performance you can add a USB based graphics card. This works fine for mail, browsing etc, but is unsuitable for games or other software which rapidly updates the screen.
  4. You can use a Matrox dualhead2go adapter. Though the VGA version seem to be limited to displaying two screens at 2x1280x1024 (presenting a single 2560x1024 display to the host).

No, you cannot do a splitter and get two unique displays (you would get 2x the same display), the only technology that supports this as of current is a display port.

I don't see your model on their site, but with Intel 3000, I am relatively confident that you do not have that.