It sounds like miscommunication and lack of knowledge all the way around. For a weld to properly penetrate its key that the area be properly prepped. The guy doing the welding should have better understood what was going on also before he started welding. The guy that did the welding shot himself in the foot and set himself up for headaches by not knowing what he was trying to accomplish. As far as getting the welder to pony up $$ for the damage that is going to be a tough call. Did he have a signed job ticket saying what was expected of him? I'm not sticking up for either with this because I feel there where errors on both sides of the fence. I do feel bad seeing a guy having his hard work damaged and causing more work.
As Tim suggests, post some pictures and maybe guys can give you more information.
