It's not the fact that it has wheels or not, but whether it is an overhead bin item or underseat. If it won't fit under the seat, they will force you to check it.
You're not going to get around that if they force you to check bags. If you are consistently asked to check your bag (and it isn't oversized) then you are probably always boarding last. Are you group 9? That means you are purchasing the basic economy tickets and they don't include an second cabin bag. In that case, spend a little more for main cabin tickets. Otherwise, try choosing a seat further back in the plane. That means you will get one a little bit earlier, and have a better chance at not running out of room.
If you travel that route twice a month, though, have you joined AAdvantage? By the end of the year, supposing you meat the minimum spend requirements, you should get at least gold status and that will give you earlier boarding.