Almost every problem fix is the same. Start small and work your way up.
target a mob on your main
do /target MainName-target on your alt and see what happens
If you get the correct mob on your alt, then do /cleartarget and do /cast [target=focus-target] Hunter's Mark on your alt
If your alt casts correctly then do /cast [target=focus-target] Serpent Sting on your alt

Things that can go wrong: your alt isn't getting the target soon enough and it errors out and no attacking, your focus isn't set correctly, you spelled the spell wrong on the alt, you probably can't continue to attack a focus-target, you have to /assist to continue to attack (IE, you can cast 1 spell, but not continue to attack a mob you don't have targeted...wanding, shooting, melee, channeling, etc all need a target, not just one in a option, an actual target)

Hopefully you will notice something along the way that is not working correctly and you can fix it. Hope that helps and good luck.