Bet more preflop, raise $15 - $20, whatever the table threshold for calling is. $10 seems way too light. Also, is the open in your 1/2nl game $4. Even though most games "say" they are 1/2nl, the open is usually $4. And if that is the case, you can EASILY raise $15 - $20 preflop.
As for the flop. You can always overbet flops in 1/2nl. Players don't really think in terms of the size of the pot, but rather about how many chips they have and how they have more than enough chips to call $30 or $40 on the flop. So easily bet pot or even 1.5 x pot. They will put you on "AK" and call you down as long as no Ace or King is on the board, so you really want to take advantage of that.
If you had bet more preflop and on the flop then you could have shoved turned.
As played, the turn is a sick card, but you can go for a razor thin value bet or a check back. I think you can make a case for either line.
River is an easy check back.