sibling rivalry or a terrible two testing the boundaries?

[Tuzz]

My older DS is 2.7yrs my little one 7 months.
My older son is finding it hard to resist the temptation push the little one over or snatch his toys away. He does it any time he potters by. The baby might be sitting, standing up at the table or in the bath. Tonight he grabbed him around the chest/neck rolled him onto his side and then dropped him face first into the water. All of it done in split seconds when i am there or have just left the room (not in the bath of course).
I am not always able to react calmly. when i can i hold him, look him in the eye, tell him i love him, that we don't do pushing and ask him to say sorry. Tonight in the bath i got him straight out wrapped him in a towel and put him on his bed and explained why he had to stay there. I would rather praise than punish but i am finding it hard and sometimes after the 5th push of the hour i do shout at him or like tonight in the bath i let out a scream for him to stop.
Is he doing this to test my boundaries/get a reaction and without the baby would be doing this to the dog/his toys/anything to get attention or does he really want to hurt his brother?
should i bring in the naughty step for this or encourage him to be kinder and more gentle by rewarding the things he does/could do for his brother? i am thinking 10 stickers to get a toy.
What have you done to discourage this kind of behaviour?

I've a slightly younger boy and no little one yet, but we respond to any kind of physical aggression with a stern "no!" and an order to go "have a seat" - which means sitting down in the hallway away from toys and us to calm down / have a think. We've not called it a "naughty" place, but it is punitive and he comes back only when he's calm and says sorry. We then always have a little talk to be sure he knows what he did wrong and why it was wrong - I.e. "Hitting hurts people". And we encourage him to talk about the emotions which are ok "you were cross" vs the action which isn't. This works well for us - it takes him out of the situation, gives us a chance to calm down when he's hit us, and doesn't instantly give more attention for bad behavior. For me, it feels right to have a punitive stance about behavior that's really isn't acceptable, like hurting others, doing very dangerous things, etc.

In terms of your question I'd say yes to both. He's testing your boundaries and he's testing out the relationships between you three. It sounds to me like its all pretty normal stuff and you're doing well. I agree that you should look for and reward kindness, but I also agree with HJBeans that a punitive stance is also sometimes appropriate, even at a relatively young age.

My DS1 is a bit older but we spend quite a lot of time actively encouraging him to see himself as a loving older brother who takes care of the baby - he can help the baby (and get loving praise from parents) by getting toys and holding hands and also helping tickle the baby. When he's lovely to DS2 we always say 'that's so loving and DS2 loves you so much'. Seems to be reasonably effective...

It is hard for you but unfortunately your 2.7 mth old is only a baby himself and cannot rationalise his emotions.
He is reacting with jealousy and it is a very strong emotion. I am sure that you are trying to be patient with him, but if you overreact to his behaviour, as he is not entirely sure why or what he is doing, anger from you will fuel his insecurity even more.
Try and ignore his negative behaviour as much as possible and react calmly.

That does not mean that you should not say anything. Pick your battles. If you come down heavily on the side of the baby, by over reacting, shouting, pulling DS1 away etc, it will reinforce the idea that you prefer the baby to him.
He needs a lot of reassurance at this time. Words will not be the same as deeds.
If you could factor in some special time alone with DS1 to make sure that he feels reassured that you love him.
He is too young to be plotting and planning to make your life miserable. So try and count ten and empathise with him. Jealousy is such a terribly strong emotion.
It is hard and we have all been there. You just feel like throttling them sometimes when you feel exhausted and they are all squabbling, etc.

However, the more patience you show them the more you will be rewarded in shed loads when they are grown up.

By being patient You will be giving them what is absolutely priceless, a happy childhood.