That's not uncommon TBH for them to ask for that. Even though y'all are family generally speaking all should be listed on the policy. Some insurance companies don't require this of minors but in your case your kids are not minors. I understand why they want to see all members listed on the renters policy if they are the same members who are applying for a lease even though y'all are family.
Ugh yeah see that would be confusing. They probably should have made that really really clear OR not use an e-mail so close. Makes me wonder if others have had issues with that.
Well that's strange isn't as the other guy said they did have access to it but they just didn't like to have to pull stuff through it. I get it for efficiency they don't like to have to monitor a main corporate e-mail but if the other guy you spoke with said they could go in and pull it up but just didn't like to do that sounds like this other woman just doesn't want to do it or doesn't know how to. Either way even if there was an error on your part you'd hope they would be understanding and try to work with you.
This does sound like a hassle. I would def. call them today. I hope you can get some good communication going