First of all realize that all kids hate their siblings at some point in most days. Siblings are always vying to be favorite - that goes back to the beginning to time (Cain & Abel). Also keep in mind that he did not ask to have divorced parents and have to go back and forth between different homes. One where he's completely adored, and another where the little sister is completely adored. Can you imagine if you were in a similar situation with your husband? Every other week you leave your comfortable, familiar home to live at his other wive's house? ...and there are times that he shows a clear preference to his new wife? Wouldn't you want to hold the new wive's head under water? This would be a tough situation for an adult to handle let alone a 6 year old. And of course, to complicate things, his mom is an only child, as is he. And you, as step mom, see him as a neccessary, but unwelcome distruption in your home - and don't think he doesn't feel that - whether or not he can understand or verbalize it. I'm not saying that your feelings aren't valid - they are. Having your husband's child come in to your peaceful home every other week and create discord is understandably difficult. But - you are the adult - he is the 6 year old.
Just like when you bring a new pet home, the old pet has to be shown extra love while introducing the new puppy or kitten.
First I'd suggest that when it's transition time your husband and his son go spend some time together alone before coming home. Your husband should pick him up - go have pizza alone with him, go to a movie, to Chucky Cheese, a play ground - whatever it is that makes him realize he's special and loved. He needs to know that he's loved by his dad. I'd also suggest that you spend some time alone with him - it doesn't have to be a lot - but you should still. Take him to the play ground - when your daughter takes a nap play a board game, etc.
When your SS and daughter are playing together keep an eye on them closely. I recall reading a book about introducing a new baby into the family and they advised to NEVER assume the little one is going to be safe with the older one. Until kids are around 10 or so they don't truly understand the permanence of injury and death. They only understand scraped knees, twisted ankles, bonked heads, etc. He wants to hurt the little one becuase he feels hurt - but he can't take the next intellectual step that holding a 3 yr old under the water can cause permanent brain damage or death. (PS - my brother who is a year older than me seemed to always be holding me under water...)
You and your husband need to conduct yourselves calmly after an indident -the screaming (although understandable) is completely ineffective and just scary . Your SS needs to feel more pain for harming little sister than the original pain he felt which caused him to try to harm her. So maybe a spanking is in order - but only by dad and only AFTER dad's calmed down and able to explain why he can't try to drown another person - little sister or stranger. Spakings are on hineys only, never face, head, arm, etc. Then your husband needs to hug and hold his boy and tell him how much he loves him - no matter what he'll always love him - but that he's not allowed to harm other people - including his little sister. Dad must also add that the same rules apply to little sister - so if she does something that puts his life in danger that she'll get a spanking too.
My daughter, who loves her younger brother, had times of trying to harm him when they were young. I've read stories of older siblings trying to flush baby down the toilet, hang baby out the second story window ready to let go, etc. Kids need to be supervised when they're with their younger sibling and even without the different homes, split custody, etc - it happens in every family.
Finally - do everything you can to foster their appreciation & love of eachother. Help them do things together, have your SS teach his little sister something special he can do that she doesn't know how to do. Encourage him, tell him you know that he's going to be the big, cool brother that his little sister is going to want to be like. Ask his opinion - what can you show your little sister to learn that you're an expert about? Kicking a soccer ball? running really fast, climbing the monkey bars? Encourage him to accompany her down the slide since he's a big brave, kid and she's just a little girl, etc. Supervise and look for good behavior so you can praise it when it happens. Positive reinforcement works SO much better than negative reinforcment. Expect good behavior, explain what it is, coummunicate that you are so happy when you seem them playing together, tousle his hair, give him a hug, give him ice cream or m&ms when you see him doing the right thing. He will WANT to do the right thing becuase it feels good and he gets positive feedback for doing so.
But, if his behavior doesn't improve as he gets older then get him into counseling. Your husband has a responsibility to his son as much as he does to his daughter and by marrying him you'd taken that on.
Good luck mama - raising your own kids is tough, raising someone else's kid is really tough.