You do have some childcare options. Call your local command's Child Development Center office (that's the Navy term; what each branch may call it can vary). They can hook you up with 24/7 childcare options both on and off-base.
As far as 8-5 work: doctors/private practice offices, medical clinics, urgent care clinics, outpatient programs, partial hospitalization programs, ambulatory/same day surgery centers, school nursing and community health are just some options. You can also look for facilities that do 4 to 8 hour shifts...there's not as many out there than those that do 12s, but they are out there.
Another option is to sign up for registry nursing and only be available for weekday daytime shifts. That may or may not entail 12 hour shifts, and it may not guarantee you enough hours, especially if your household depends on the income you bring in. But it's an option.
Last, if you quit your last job to relocate specifically to be with your spouse, you may have hiring preference with military facilities. This does NOT guarantee you a job--for example, if the job requires specialty/greater experience than what you have or offers hours that you are not willing to work, it's not going to help. Nor is the military obligated to hire you over a non-military spouse. But if all things are fairly equal between you and other applicants, it could give you the edge in the hiring process. And there are some civilian jobs in the military/VA that have the hours you seek.
Heads-up: the hiring preference window is for a limited time (unless they changed the regs when I wasn't looking). If you moved fairly recently, you're good. If you moved last year and are only getting around to looking for work now, you might not qualify any more. Also, if you already have a job at the new duty station and are just looking for another job with better hours, you do not qualify for hiring preference. Contact your MWR office to find out the specifics.
Best of luck!