Is it possible to pursue a career in teaching, and then later in life, a career in nursing?

You absolutely can pick a direction and work in that area for a while, then make a change. You will likely need to go back to school to get more education. People often have a 2nd career after they are done with their first.

Have you thought about going through with your plan, but in reverse? Get your nursing credentials and then, after gaining some experience, teaching within that field? Nurses need teachers, too! Nursing schools are always hurting for clinical instructors, and taking on, say, an adjunct faculty position at a community college, typically doesn't require a teaching degree, and allows you to keep working within your field of expertise.

The trouble with your original plan is that you've picked two career fields that typically require lengthy and expensive certification... and then require continuing education in order to stay certified. Going back to school for a complete career change after a decade in the workforce is certainly not impossible, but it is very, very difficult. Marriage, children, and shifting financial circumstances all play a role, too.

Nearly all career fields, however, have a need for good instructors, teachers, and mentors within those fields - in other words, you do not have to have a teaching degree and work in a classroom in order to teach something worthwhile. I'm a commercial pilot, and never envisioned myself as a teacher, but I spent six years as a flight instructor, both at a university and in as a civilian contractor for the military. It turned out to be some of the most satisfying work I've ever done.

In other words, it is possible (and probably desirable) for you to have a "second career" as a teacher without doing anything so disruptive and expensive as actually switching careers. Look for teaching opportunities at any job you ever have - I guarantee that they are out there!