In Dine Out it’s unfortunately not possible to hire your own Sims as employees but mcrudd at the official Sims forum has found a way to at least create your own and use those.
Be aware that any Sims you play will immediately loose their job and you need to rehire them.
Steps to take
A complete tutorial with lots of pictures can be found here: Tutorial on how to hire your own sims you made, to work in your Restaurant (by mcrudd)
Mods that help with the issue
- Hire certain Sims (incl. Family Members) at Restaurants by LittleMsSam