Sounds like you may have a major job ahead of you. Take your rudder home. Drill small test samples starting in the suspect area and widening until you are confident that you are past the wet core area. You'll know the difference between wet drill shavings and dry ones. Once you have determined the extent of the damage, drill plenty of additional holes in the region of wet core. And let it sit in a dry warm area for a long time. Months if you can. Use a heat lamp to warm the rudder (but only when you are home). When you are confident that the core is dry and not delaminated from the skin, fill all the holes with epoxy. Fair and paint as normal.

If you have delamination problems (usually due to the core being wet for along time), you may find that the only fix is to strip off one side of the fiberglass skin, replace the core, and reglass the rudder. Lets hope thats not the case.