Connecting Two External Monitors to One Laptop

If I'm correct, you will not be able to use all three monitors at the same time. If you hook up two monitors to your docking-station, you will not be able to use the laptop screen at the same time. If you only use one external monitor, you can still use the laptop screen. This is due to limitations of the GPU. I have a Latitude E6510 with a docking station and experienced the same thing.

If you absolutely need to use three monitors, you can maybe look into "exotic" solutions like using an external USB graphic card.

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).