Hi yorkie family, I am new to the forum and have two new yorkie babies..my daughter and I went to pick up one and left with two

they are girls and littermates.
They play together but they also get right vicious with each other. I assume since they are away from all the dogs at breeder now they are pushing for dominance. They are only eight weeks old and we do separate them and correct them when they do this. We do crate them together and from what ive read this is a controversial subject. We feed separately and they do have time away from each other so they will bond with us and not just each other however we want them to like each other and get along. We love them and will not get rid of one...we are determined to make it work.
Any advice you could give us would be comforting and helpful. Should we correct them or stay out of it? Should we crate separately? Thanks.