Wehad a plumber in to fix and all he did is shim the toilet. We cannot caulk around the toilet because on one side the toilet there is a 1/2 inch gap and other side 1/8 inch gap

We had a plumber in to fix Fix what? What was the original complaint? What material is the flange and pipe? The flange needs to be lowered. Does your plumber have enough experience to do this? Do you want to try yourself? Let me know, Tom