Submitting a paper to a new journal with responses for the rejection to the first journal
I wouldn't do that, actually. Use the comments of the reviewers of the first journal to improve the paper as usual. Simply submit the revised paper to the other journal. 

It is actually better that they look at it with a fresh viewpoint, rather than having their view possibly clouded by the opinions of others. Let your paper stand on its own. 

You will get additional comments, of course. Hopefully they will also help you improve it further.