First thing is first… You need to know everyone’s stacks before you raise. If a short stack is going to shove on you, so be it. Youre committed.
As for your raise, it was light. I know it is a “1-2” game, but most tables have “a number.” Most 1-2 games I play have a much higher number. The lowest number I see at my tables is about $15-18 for raises. Ive seen the number be $80 at 1-2 before people would fold. Personally, I would have limped in your early position.
Either I am going to play this for a very small pot, which I dont mind folding due to a huge bet that comes on a later street. Or, someone is going to raise preflop, which I am hoping, so I can play this for my entire chip count. If someone raises preflop, I will make it hurt to call my re-raise.
Most 1-2 games are straight forward. They will have a pocket pair or AQ/AK if they call you. Due to your re-raise, you should be pot committed. So, shoving on the flop gives you 2 ways to win.
Im not saying your read is wrong, because it is likely, in most cases, that you would be correct. I just like getting in as much money preflop with Aces, so I can shove on the flop because it’s a pot size, or less, bet.