Hi Jason, This is something you could perfectly create in Filemaker.
I would suggest you download a trial version of filemaker. Then you have 30 days to experiment.
Then watch this video: http://www.youtube.com/watch?v=5v2EzvaWyBk
To learn a little about how Filemaker works.
You should be able to set up your fitness database with ease.
About sharing the database:
I have no experience with standalone solutions. I would think the best solution would be to get 2 licences for Filemaker Pro and put them on those two computers.
If they are on the same network you can share one file between the two computers and they can both be working in the file at the same time. Adding records, updating data...
Then if you want you could add all kinds of other functionality in your database (invoicing, todo's, expenses, reports, ...) to really make it a full administrative package. But then you'll need to learn a bit more about how to develop in Filemaker.