You have a prickly pear cactus.* To transplant you should fold several layers of newspaper and wrap the plant with it.* You can also break off some of the pads and transplant them where you want them.* You can also use tongs, but be careful not to puncture the pads.
I would suggest you edit your post and remove your e-mail addy from public view.* That's how you get spam and most folks that answer questions on public forums don't write to private e-mail addys.* You can receive instant e-mail notification of a reply when you make a post.* If you didn't do that you can click on 'Watch Topic' at the bottom of the post.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.