Job change need advice...

I am a new nurse and took a job across the country. I wanted to try something different and was hired for a progressive care position. While I love the people I work with the unit is not progressive care but really med Surg telemetry. Had I known this I would have never taken the job. The staff agrees this was a goal that the unit would be progressive care and that is why it's called that. So there was some misunderstanding in my interview process there. I really moved for the job and so this is very difficult for me. In addition I do not like the area and the move in general has been a disappointment and a mistake. I have been offered a position in the unit I've always goaled for in my home state... I have worked at my current job for almost 3 months and I am still within the "probationary" hiring period. My question is what do I do? Do I need to stay at my current job and tough it out and let this opportunity pass in order to save my credibility on my resume? I feel terrible and know I've made poor choices and put myself in this position so please no tough responses (I have learned my lesson). Do I have to list my current job on my resume if I leave since its within the probationary period? Will it always show up as me working there on a background check? I have never had a situation where I did not stick with something and I do not want this to follow me and look like a red flag on my resume forever... But I'm also tired of being unhappy. Please give me some advice here.
If you're going to leave, it's better to leave sooner rather than later (and the whole point of a probationary period is that either party is free to end the relationship at any point for any reason). Lots of "new nurses" struggle a little at first with finding a job that works for them, and it makes sense that you might want to return to your home community. I think it would be reasonable and understandable to resign with the rationale that you and the unit are not a great fit and being that far away from your family and home community is not working out the way you anticipated. If you really have a firm offer for a job at home that you really want, I would take it and go. It's not likely that doing that is going to seriously hurt your future career. However, it would be a really good idea to stay at the new job for a serious amount of time before making another change.I would not leave this experience off a resume' or job applications in the future, just in case it does turn up in a background check in the future and someone might get the idea you were attempting to withhold the information. As I said, the scenario you describe is not uncommon for new graduates and it would not be difficult to explain why you wanted to return home (without saying anything negative about your current employer). Best wishes!
If you already have another job offer, why are you concerned about your resume? High tail it out of the place that misled you and go do the job you want.Honestly I would be very surprised if a background check company found a 3 month stint in another state if you didn't commit any crimes. But, if it worries you, put it on the resume and explain that you were misled in the application and decided to leave.You're overthinking the importance of this job. Get out now and go do what you want, future employers won't give care about this.
RE: leaving things off of a resume.... If you receive a paycheck with FICA deductions - that job will show up when a prospective employer runs the type of background check that is required for healthcare. I have never encountered any organization in which 'falsifying employment application' was not grounds for termination. So - it's better to be honest on an application. As pointed out by PPs, this type of situation is fairly common for new grads who are just starting out in their careers.