This is called using proxies to edit with. DV widescreen is very easy on your CPU and will edit like butter.
If your computer wont edit your .mts files, you will need to convert them all to something Vegas can use on your PC, being Cineform or DV.
Render each to the same name, in the same folder and the extention will be avi. If you’ve already started a .veg with the .mts, you can replace the file by clicking on it in your project media tab and select replace, then point to the new .avi file with the same name. Edit with these avi files, then use the same method to replace them with the original .mts files and render. Best done just before you go to sleep. LOL
There is a program called Gearshift by Vasst. John Rofrano, also a Sony Vegas leader here at the Cow workes for them I believe. Feel free to jump in John, maybe tell her the benifits on using it versus my method.