I agree with Crystal. I'd trust your vet. Homecooking is tricky which is why it is important to get frequent bloodwork done to make sure all the nutritional needs are being met. I would also be curious how he detected the iodine deficiency, though.
Are you following a recipe prepared by a nutritionist? Are you adding any other supplements besides the AE Multivitamin? I homecook and use the AE vitamin, but I also have a whole list of other supplements I have to add.
Kelp is an excellent source of iodine.
There's a little on page 9 about iodine needs in a dog:
http://dels.nas.edu/dels/rpt_briefs/...tion_final.pdf