I like
Charlotte Juliet a lot. I think
Lottie is a fine nn. I don't think of a Grandma but I do think of a little girl(I think a few books use this name on small child). I think you should use
Charlotte as the proper name because
Lottie Juliet doesn't flow as well to me. I don't like the other combos though. I don't mind
Josephine nn
Josie but I don't like it with
Juliet (too much alliteration). I don't think there will be a lot of teasing.