I purchased this vehicle and really want to keep it. It is a good looking car but turns out to have rust in the doglegs. My question is if there is a way to repair rust that is longlasting. Is cutting metal out very bad?

No, cutting metal out is really the only proper technique for rust like that. Fortunately there are inexpensive patch panels available:

http://www.tabcobodyparts.com/html/167.htm

First I would like to thank you for the reply. Also, is the car worth keeping if the doglegs are that bad off? It seems like the rest of the car is pretty decent. I really wanna keep the car and put it on a rotisserie at some point. My question is: Is this car worth doing that to?

Short answer is Yes, it is worth saving with bad doglegs.

However, you should be aware that usually, the rust that you can see is only the tip of the iceberg. Meaning that as you go to repair the doglegs, you may find tha the rocker panels have also been eaten by the rust monster. Even if that is the case, the car is still worth keeping and doing a full resto later on.

The rust areas where it gets real expensive to repair are the frame rails, floorpans, and the battery tray and area under it. Also the rear hatch area, and the spare tire well.

Good Luck with your car