I am a single mom, my son is now 16. I have never had a BF spend the night with me while he was home. It is just not what I want to model to him...bad enough I had him out of wedlock, and have had to explain that to him over and over again through the years. LOL
While I don't think it is immoral to have a BF spend the night, I do think that it risks having your children, especially your youngest, get attached to this person. If the relationship does not work out then your child's heart gets broken. She has been through two of your relationships already, I would just suggest that you tread lightly and slowly with this one.
Also, don't under estimate the power of her father's opinions. She will not be able to develop her own opinions, based on life experience, for some years. So, if Dad is telling her something is wrong, and you are telling her something is right, it sets her up for a lot of confusion.
Those of us who the children live with, and who have obnoxious exes, find ourselves in a precarious place of balancing our needs with the needs of our children, and with the influence the other parent has on our children. I find, with myself, in the past, that I had much resentment against my ex for being able to live his life - i.e., go out, have GFs stay over, etc., things that I would not do. Then I got over it because it is more important to me to model the values that I wanted my son to have.
Why not just have BF spend the night with you when your kids are not home?
Good Luck!