Are soldiers sent home if they have been diagnosed with post traumatic stress disorder?

Yes: Soldiers are sent home if they can't do their jobs, and ptsd can certainly prevent that. But it doesn't require a ptsd diagnosis specifically. Ptsd is only diagnosed 1 month or more after the stressful event, and a soldier can have an acute stress reaction sooner. There are many other psychiatric issues that can also get a soldier sent home — anything that prevents "soldiering".

Not necessarily: The bottom line is that emotional numbing, hypervigilance, fight or flight re-activity & little sleep can help keep a soldier or a marine alive in combat. It is adaptive. There are many soldiers who have ptsd or post traumatic sxs who return for subsequent combat tours. The real issue is the soldier fit for duty? If s/he functions well, then removal from a combat zone is likely not necessary.