I don't think there is any way you can fold the first hand when you have trips, ace kicker, and only one overcard on the board. You have 6 outs to fill up there with little chance that your opponent would make a bigger boat if an A, K, or Q came. You have to call that bet (I don't mind your 2/3 pot bet, tho).
The second hand was another spot for a pot bet on the turn. Not sure if he folds his AA, but I'll take those odds all day long if he's drawing to 2 outs on me.
Where trips will get you in trouble is a case like a board of J66 and you have a 6 with a weak kicker. If another high card hits the board and there's some action then you would generally be wise to fold, but when it's a situation like you described above you have to bet and call them down.