Quote from xenogenetic
I have my real estate license and have my own brokerage, part-time, on the side mainly so that it helps me in acquiring more property into my rental property business. I NEVER, EVER include the fact that I hold a real estate license on my resume and suggest you don't either. I believe that employers will feel as if you might be a waste of resources (meaning employers spending time and $ training you) because you have another career that you can potentially slip into. Or, they may not view you favorably with respect that sometimes they know they will be looking for emergency coverage for shifts and with you having potentially a second career you probably will not be available to help fill out those hours.
Lastly, you have to remember that many members of the public view Realtors in a negative light, as being one step above used car salesmen. Don't assume that everyone has a POSITIVE impression of Realtors, because not all people do. It's a shame that the whole Realtor profession gets splashed by the poop water of the incompetent few, but that's the real world we live in.
Coming from someone who has spent a lot of time with HR managers, recruiters, and hiring managers from various career fields I can't disagree with this more.
While yes people may not look at realtors in the most positive manner, you can't build your resume on the assumption or fear of your potential employer being one of the "incompetent few".
Now whether or not to list your actual "license" when applying is debatable. The holding of the license itself is not too relevant to the nursing field (other than you have shown you can meet qualifications to actually hold some type of state regulated license) so it is really your call but personally I wouldn't due to its irrelevance.
The EXPERIENCE as a realtor on the other hand I would list. You have shown that you are personable, can gain the trust of people (enough that allowed them to trust you with assisting them in buying a house which is a pretty big deal), and can be responsible for the correct handling of the home buying process. Not to mention you worked while going through nursing school which is an incredible feat in of itself and shows incredible time management and performance under stress.
My point is while buying a house and ensuring a patient receives the correct and accurate amount of medication are two completely different tasks, there are transferable skills you have gained while working as a relator that you shouldn't leave out of the resume. Writing a resume can be awkward because you have to "sell yourself" or "brag" but don't be afraid to show the confidence.
Now I couldn't speak to the having to forfeit your real estate license upon hire. While I have never heard of this, I don't know if that could be a policy of the hospital or law of the state, but it would be worth doing a bit of digging to find out.