You are most definitely not being unreasonable. Bear in mind as well that you have no idea how long labour will be, are they willing to wait in the waiting room for 2 days. A labouring woman does NOT need the stress of having in-laws (or anyone) 'waiting' outside for her to hurry up and give birth. She needs the ability and support to totally focus on herself and her baby and take however long she needs to take. Basically, she needs what ever the hell she wants to get through labour.
It's not so much the insistence that the in-laws get to meet the baby first, it's the insistence that they are in the waiting room that would bother me the most. Having said that I think as part of the introduction to the family of a new baby the sibling should get dibs on greeting their new brother or sister first. As for referring to you as anal, that's just uncalled for
Perhaps show your DP this thread?