L.:
Hello! I have two young boys - my daughter is grown, so I understand your situation.
Your youngest child's punishment or time out MUST be alone. Let him scream, yell, cry, etc. but DO NOT talk with him, try to control him, or do anything OTHER THAN IGNORE HIM!
I agree that showing him what he is doing hurts someone else. Even though my children are 6 and 8 (and 22), they really don't realize what they are doing to someone else. Yes, they SEE a reaction but they really don't know WHAT they are doing. So next time he does it, do it to him - not viciously, but do it so he knows what is being done.
My youngest was "tasty" in day care - he was the one always getting bitten. He only did it ONCE to the boy he was continuously biting him and guess what? It STOPPED.
He is trying to exclude his older sibling and its working.
He needs time away from mommy. A play group while his sister is in school would be a great way for him to "share" mommy and learning about behavior from other kids his age.
I realize you are a SAHM - I was for 3 years - and the budget MAY not work for this - however, I do suggest that you enroll him in half-day partial week (for example Kindercare and other types of pre-schools offer half day and two day a week programs). This allows you time to yourself, which we ALL know Mommy's need and must have and time for your son to be on his own without mommy and learning new things.
I don't know where you live - however, there is Lake Anne Nursery School in Reston, VA that offers a WONDERFUL program - there is NO full day and it's GREAT! The teachers are wonderful, kind and loving. It's a great learning environment!
Your daugher MUST be recognized for her GREAT reaction - when others MIGHT throw a toy at him, she's VERY cognizant of his feelings and as you say, rarely responds in kind. Reward HER for not reacting in kind. Gush over her, love on her and tell your son to leave the room. DO NOT take him there, DO NOT IGNORE DIVERT his attention. IGNORE your son. He wants your attention and ANY attention be it good or bad, is YOUR attention ONLY ON HIM with a toy or something else. HE has control and he knows it.
Love on him when he does good things as well. But ensure that you give both of your children the kudos when they do good things. It's like in school where they get "caught being good" - notice it, applaud it.
Bottom line - your son needs to be disciplined for hurting his sister - there are those that say "violence begets violence". I am one that does NOT believe that. When it comes to toddlers - as they truly do not know what their actions are doing (other than getting a reaction). They need to experience (not full force) what they are doing to others.
Know that this must not change when Daddy gets home. The punishment MUST be alone time - do NOT talk with him, IGNORE him.
I hope this helps you. It will all work out.