I've been fighting poison hemlock for years.  Once you realize what it is you start seeing it everywhere. It is difficult for a couple reasons.  One is the growth cycle.  Poison hemlock has a two year life cycle.  And it is very prolific.   One thing that happens is you get a multi-generation colony.  You spray and the bigger plants keep the herbicide from effectively reaching the smaller younger plants.  So the bigger plants die letting the younger ones to grow better.

Crossbow/Crossroad (Triclopyr + 2.4-D) is the most effective.  I've used glyphosate/2,4-D and it works, but Triclopyr seems to be more effective. I apply label rates along with dish soap for better coverage.  However I do not know about applying it in alfalfa.  It would have to be spot applied.