Is there really no hope to upgrade the graphic card of a laptop?
Solution 1:
There's really no hope. There's no place to put a better video card (the existing one is integrated into the motherboard). There's nothing to connect it to (no way to get to a high speed bus or to the video to the panel). There's no way to get power to it as the laptop's power system wasn't designed for that. And there's no way to remove the heat it would generate.
Perhaps with sufficient cleverness, you could get around one or two of these problems. But there are four of them, so basically there's really no hope.
Solution 2:
If there was a model of that same laptop that had a more suitable graphics chip (it's almost certainly not a card), you might be able to get a spare motherboard from that model and swap.
Or find an upgrade path to another laptop (same or different type, but with a GPU you approve), buy a barebones one, and move your good components that work over to it. Sadly, that may still mean only the HDD will go, maybe RAM, WLAN is a tricky install and CPU often isn't socketed. Battery only if you stuck to the model/line. Unless it's a Thinkpad, you probably couldn't get one without a display or keyboard either.
In other words, laptops are mostly black boxes with very few parts you can affect inside. The GPU is probably the most tightly coupled of those parts, too.