I’m currently a practicing civilian Anesthesiologist considering joining the Reserves. What is the realistic likelihood of being able to deploy to a location abroad where my wife and children could accompany me?
Approximately zero.
I did have one deployment (when I was on active duty) with a surgical team that accompanied a battalion of Marines. We sat in Sicily while they waited for something to happen in Africa that would need a rapid deployment of Marines. We mostly had nothing to do. I was there 10 months. It was supposed to be 7, but COVID broke out and we got locked down and extended.
Before the COVID shenanigans, my wife flew to Sicily and stayed on base with me for about 10 days. It was pretty awesome. But that is the closest thing to family accompanying me or anyone I knew on a "deployment" the entire time I was on active duty, which covered the entirety of the GWOT.
Is this branch dependent? I spoke with an Army Reserve Anesthesiologist in passing at a conference who was planning a deployment to Europe where his family would accompany him, and he implied this was possible, particularly if one volunteered for deployments where families could join. I’m aware that not all deployments can accommodate families and that as a reservist, the family members joining are your financial responsibility.
That almost certainly wasn't a deployment, but rather an accompanied permanent-change-of-station (PCS) move. The military runs some overseas bases, and to staff them they will assign people there for 2-3 year periods. It is normal for families to accompany the servicemember on those assignments.
However
Reservists generally don't get multi-year PCS orders overseas. There are mechanisms where they can spend extended periods on active duty and do that, but I think it's rare.
On the active duty side, the desirable overseas duty stations are, well, desirable. And that means lots of people want to do them. Which means new joins don't get to do them, because those spots typically go to people who've negotiated a nice duty station to follow some **** duty station.
If overseas family travel is something you want to do, honestly, your best approach as an anesthesiologist is to earn a ****load of money working hard as a civilian anesthesiologist, then take a 3 or 6 month sabbatical, get everyone a passport, and take them overseas to exactly the place you want to go.