I think the most effective way of doing this is like others have suggested, get a white noise machine, put her in her own room and leave her until naptime is over. She is 12 months old and she needs to sleep. It kinda sounds like she could do without the morning nap too. When you check up on her don't let her see you...I found that with some kids they NEEDED me to go tuck them back in to be able to go back to sleep and wouldn't until I did. So I stopped going in at all, only checking on them through the video monitor and they learned to fall asleep on their own.
As for dcm, instead of ASKING her if it's ok to do certain things, why not just TELL her that "this is what we're doing now". When I approach things with parents I don't really ask their approval. This is my daycare and I think they should trust my judgement as this ain't my first rodeo. I get that some parents don't like CIO, but at the end of the day the child needs to learn how to get to sleep on their own. You are teaching them a SKILL!