I can relate to your situation when it comes to crummy work schedules. My hubby also works Monday through Friday (only he gets home significantly later than yours) and I work weekends (although not as long of a shift as you). So, yeah, time is super important and communicating about how you're spending your time is important, too. Add in kids, and I'd be going nuts.
Are you over-reacting? Not really (IMO). Your house is your space, so you have a right to know when/if people are going to be in it. It's also his space, though, so if you're not there it's not really your place to ask him not to have someone over. Unless it's someone who makes you feel unsafe or have a good reason to not want in the house. Not wanting her there when you get home from a shitty day - fair, but if it's their date night you can't get upset if he's not there either.
Do you two set aside specific date nights for yourself? If not, start! You can't ask him to just automatically dedicate every night to you unless you give him permission to see his girlfriend. If you need x amount of time, tell him that and then set up a schedule.