During Season 2 of TNG, Dr Pulaski takes over as chief medical officer for the year. I notice that she seems to be a rather down-to-earth sort of person, rather reminiscent of Dr McCoy. I also note that she has a sort of banter with Data, also like that between Spock and McCoy, although theirs is not as heated as Spock and McCoys. I was wondering if there was any reference to an intentional parallel between these two's relationships made by the actors/directors/producers at all?
She was indeed brought on the show with the intention of mimicking the old "Big Three" interactions between Kirk, Spock, and McCoy - but the actual catalyst for the change was behind-the-scenes drama between the producers of the show and Gates McFadden.
Pulaski's character is very directly derived from Dr. McCoy; in addition to simply watching her performance and seeing the obvious influences, Wikipedia is clear on this:
The character of Katherine Pulaski was modelled on Doctor Leonard McCoy from Star Trek: The Original Series, including a fear of transporters and a dislike of unemotional colleagues (in her case, talking about or to Lieutenant Commander Data often in cynical jest).
Memory Alpha makes the reasons behind her arrival and departure clear as well; essentially, Gates McFadden had a falling out with the higher-ups, Diana Muldaur stepped in, decided she didn't care for it either, and as it happened Gates and the producers had resolved their issues, so they swapped out again.
In 1988, Muldaur was cast as Dr. Pulaski for the second season of Star Trek: The Next Generation as a replacement for Gates McFadden, the actress who played Beverly Crusher in the first season. McFadden had some sort of falling out with the show's producers, especially Maurice Hurley and left (or was asked to leave) the show, and Muldaur was brought on board. However, following the end of the second season, the issues with McFadden were resolved and she returned to the series. Muldaur's last appearance as Dr. Pulaski was "Shades of Gray", the final episode of the second season. On 20 September 1988 Muldaur was interviewed and these interviews were later published on the TNG Season 2 DVD in the special features "Mission Overview Year Two" ("Diana Muldaur", "Gene Roddenberry") and "Selected Crew Analysis Year Two". In these interviews Muldaur told that she had moved into the high desert Sierra Nevada with her husband in 1988 when she got a call to work on The Next Generation and couldn't resist.
Ultimately, however, Muldaur found working on the show an unhappy experience and it wasn't what she hoped it would be. She stated that there was no imagination on the show and she felt that everyone was out for themselves and she felt they weren't happy she was there. During production of "Unnatural Selection", she and co-star Patricia Smith swore they would never work in Science Fiction again due to the prosthetics the actresses had to wear.