If you're already an initiated member, you won't go through Recruitment again because...well, you're already an initiated member. I don't understand the "Will I get to be a DG again?" question.

If you haven't been initiated yet, you can go through Recruitment one year after you drop your NM-ship. Your chances for another Recruitment might be different though as there's no guarantee that you'll receive a bid from DG again. Your class standing will probably change after a year. If you've already been initiated...well, you know the obvious.
I've seen chapter sisters go inactive for various reasons who have the intention of coming back to the chapter (or transferring to another one). At this time they paid a set of inactive dues and notified us of whether or not they were coming back, if they wished to affiliate with another chapter, or if they wanted to be automatically placed into alumna status.
breathesgelatin does illustrate an affiliation policy that is similar to ours. The first chapter writes a letter of introduction, the receiving chapter's Executive Council (or whatever you guys call it) then meets to discuss (Can they take in more members?, How can she be benefitial to our chapter?, etc.) and if they approve (some chapters and orgs. have to have a unanimous vote, some dont) they'll notify you on what actions need to be taken. I know for us, there is a small fee involved when a member wishes to affiliate.
But I reiterate, there is NO GUARANTEE that you can automatically affiliate. Not trying to be mean, just throwing it out there that there could be a ton of factors that might prevent you from doing so.
But then again, I'm an Alpha Gam, not a DG...so your best bet would be to talk to your Chapter Advisor and see what your options are.