"Why bless your heart alive" might mean that the charecter is not only glad to be alive, but is kind, generous and other heartfelt things. But the next part "how late you are" might mean that the charecter has done somethings in his/her past that oppose those "heartfelt" things. The person who is speaking, is reminding the other person that she is "late" in being kind, generous, etc.
It relates to "we'll never mind so long as you are come" because that means, we won't mind what you are, as long as you have overcome something.
Hope this helps!
