I suspect it's not your mouse that's the problem. I have a tablet but I probably use my mouse more in Inkscape as, for most things, it's just as easy. I think it's probably just unfamiliarity with the software that's holding you back.

Looking at your map, the vast majority of your buildings are simple shapes and they shouldn't be hard to draw. Have you tried duplicating rectangles once you've got them in place, i.e. instead of drawing a whole new shape and positioning it from scratch, just hit Ctrl+D on an existing shape, then drag it over a bit and use the selection arrows to tweak the size or rotate. You can also use the snapping tools to help you align objects (be selective with the snapping options. Do *not* turn them all on or it'll be a nightmare to position anything!)

The other thing you could look into is Cloned Tiles. You create one shape, then clone it. You can make the clones bigger or smaller, rotate them, and change their colour, but you can't alter their basic shape. I think cloned tiles are a little less resource-intense, which can help if you're creating a large image with lots of nodes.

Anyway, just some thoughts on how to make the workflow easier. I love Inkscape and find it really easy to use, so it's worth sticking with it and trying to get over that initial learning bump. Good luck and I hope you'll post some more updates as you work on your map.