Point of clarification....your EOS T2i is not compatible with FD lenses. Those are manual focus lenses that are compatible with Canon SLR cameras made before 1987. Your camera, like all EOS cameras is compatible with EF lenses. Your camera is also compatible with EF-S lenses as well.
I can see why you may want to upgrade from the 18-55mm lens. It certainly isn't a top quality lens and it does feel a little bit like a toy. The problem is that to get something 'more sturdier', you will likely have to get something in the $400-$500 range.
You may be able to find a used Canon 17-85mm lens....maybe around $300-$400. It's a better feeling lens than the 18-55mm.
If you really want a lens that is much better over all, I'd suggest looking at the Tamron 17-50mm F2.8. It's got a maximum aperture of F2.8 and it has really good image quality.