I think doggie daycare is a wonderful idea as long as it is a reputable one. You can start by just leaving her there a couple hours at a time instead of a full day. She will definately be nervous and scared the first few times, but hopefully after that she'll feel more comfortable (and know that you will eventually be back to get her).

If it were me, I'd tackle one problem at a time though. The doggy daycare will make her nervous because of the seperation anxiety AND because of larger dogs. I would try to address one or the other myself before putting her in a situation like that.

If you have any friends with medium sized, gentle dogs, you could start exposing Millie to them. I would start out with dogs who are just slightly bigger than her and work your way up. Try to make sure (I know you can never be 100% sure) that its not a dog that Millie will have a negative experience with. Ideally, probably a calmer dog with good dog manners.