I always assumed Leslie Ann Down must-have demanded to be in the opening credits for her season 13 stint, UNdeservingly so! I never liked her character and she is a mediocre actress IMO. That must have been a contract demand on her part as other characters had way more appearances and multiple seasons then she did, as discussed above. They even had to lengthen the theme song that season with that little melody repeat to accommodate.
She was likely signed on and paid to do 13 episodes in the 1989-90 season with the option to extend her contract into season 14. When her character didn't exactly work out (and they ended up using her far less than that) it never happened. I assume they had hoped with North & South being popular a few years earlier that it would rub off on Dallas which was free-falling at the time.