Yes, colostrum is a laxative and you should expect your toddler to have diarrhea until your colostrum disappears (I was told this from a LC). Actually, she told me that this happens before you have your baby (colostrum can come in as early as 20 weeks pregnant or so).
As for the diaper rash, lots of nakey time and breastmilk. If we're going to use a cream of some kind, we love Magic Stick when we're using cloth, and when we're not, I like Lansinoh diaper rash cream.
SAHM mom to 3 wonderful kids!