Hey,
Firstly I am by no means an expert but week 4 of my homework says I have to evaluate someone else hand and as Pocket 3s is my fav hand I thought I'd give it a go!
Preflop - I would have played it exactly the same way.
Post flop - Here I would have played it differently. I dont like the call in this spot. The flop is co-ordinated with a possible straight and flush draw and the Q may have hit the preflop raiser with an AQ type hand - His continuation bet certainly represents that. Equally due to the small preflop bet sizing its possible that the call by the button was purely speculative with anykind of Ax suited or suited connector type hand.
So in short here I would raise and probably 4 bet it - To put maximum pressure on UTG+1 as i would suspect AK, AQ or middle pp with 2.5x preflop bet. It will also deny the odds to BU to draw for most of his hands. Its doubtful he hit a set of queens ( no preflop re-raise) and if he has fours - thats poker! Most likely flush or straight draw Axs
Turn - thats not a great card! ( I think you have my luck with sets!) Again I dont like the check raise - He may have completed his straight! Personally if I had raised the flop, I would barrel again here. If I had played the way you had, then I would check call. I wouldn't want to see an all in shove.
River - a little irrelevant as you are already "all in." I see you kept the result. Another horrid card as you are now beat by any of the Ax he may have called with. Check call for a cheap showdown here.
Final thoughts - I use to play my sets the same way as you multihanded with the thinking that if I strung them along I could mke more. This happended to me more often then not and I have found it it far better to bet out or raise on those kinds of flops then to simply call.
Hopefully this helped and if not a real player will evaluate later!
Rapier