Accepted position but now other offers

I accepted a new job after having multiple interviews and no luck. The position I accepted is only every other weekend and I was looking for more full time and the DON knows this but thought because I needed experience that she would hope that I would take it with the hope of getting more hours down the line. I have two other places that I have interviewed at this week and I think they went fairly well. I am supposed to start orientating at my new job next week. So my question is is if I happen to get another offer while on orientation at my job how bad would it be for me to accept another position and let them know that while I really am thankful for the opportunity something with more hours right away has become available.
Just be honest and as cordial as possible. Your boss should understand, particularly if she new you were looking for a job with more hours. You may even want to arrange to remain on staff as PRN with your current employer after you switch jobs...It happens all the time.
Hi Jessica, you honestly get MORE experience with MORE hours. Imagine being a nurse there and having the same (little to no) nursing experience and you've been there for a couple of months...it's unacceptable and the DON should trust you enough to give you more hours or give you more training. So I'm saying all of that to say it might be bad to abruptly leave but it's understandable and almost necessary. Just try to leave on good terms and keep it simple, say you have personal obligations or demands that prevent you from meeting the job requirements and focus on the next job. Good Luck.