Frankly, being ex-military will probably put you at an advantage... they see that you have already been out in the world serving the country. They are used to having multiple college transcripts to deal with in that case. They also know you are ready to settle down at this point, and they won't have to deal with someone who doesn't know what real life is like.
Most high school students apply to multiple colleges anyway.. my daughter, when she finished her Bachelor's, applied to 5 different universities for her grad program.... she was invited to 4 of them for a recruiting weekend (she is working on her Doctorate in Microbiology), and was accepted to all 4 of those. She ended up choosing Johns Hopkins.
I think they will see determination to follow through, especially since (if I understand it correctly) you are utilizing several different colleges to get your requirements finished as soon as possible.
At any rate, I wish you the best of luck! I don't think you will have too many problems... but, understand that slots in most nursing programs are pretty competitive.. it may take a couple of semesters of applying to be accepted.