How does the timing on these two cards work? Is "After your turn begins" the same action window as "At the beginning of your turn"? So if I had a Vile Sorceress in play, I could reduce a target unit's hit points from 2 to 1, then return it to the owner's hand with Har Ganeth?

Yes, you can!

They're actually a single timing issue and YOU, the active player, decide the order in which they resolve.

You can definately do this combo, but keep this in mind. Any forced effect goes off before any action. So, since the Vile Sorceress's effect is forced, that will happen first. Then the action will go off after. DB_Cooper is correct in that if you have multiple effects on your turn, you get to choose the order. So if you had another beginning of turn action (like Bloodthirster) you would have to resolve the bloodthirster and vile sorceress actions first (in whatever order you choose) then take the Har Ganeth action.

Hope this helps

Okay... That's what I thought...

Now for an extension to the question...

I have Har Ganeth in my Kingdom, and 2 Vile Sorceresses in my Quest. My opponent has a Lobber Crew in his Kingdom. At the start of my turn, if I use one of the Vile Sorceress's abilities to reduce the Lobber Crew's hit points to 0, does that opponent get to trigger the Lobber Crew's action before the second Vile Sorceress triggers? I assume that if they do not get the chance in this window, they would never get the chance.

Can't respond to Forceds with Actions (such as Lobber Crew). When going against DElves, 1HP units have a very short life expectancy, 2HP bit more but still removable (or back-to-handable).

With 2 Vile Sorceresses I'm allowed to kill a unit with 2 hit points at the beginning of my turn, am I not? So in this case there is really no need for Har Garneth.

Philos said:

You can use it on a unit which formerly had 3 HP, after targeting it with both Sorceresses.