The trolley looks a fine size, but yeah you'd get away with CND tote and a weekender bag, just have to be mindful of things knocking about everywhere - I managed to break the pump part of one of my CoolBlues.
For example on pedicure day you'll be bringing your PEP products, 6 hand towels and a pedi bowl (or washing up bowl) and a ritual tray (includes jug, little bowls, a tray, decoration bits like little stones) and then you'll get all your pedi stuff on the day and they're fair sized tubs. For pedi day I took a holdall 'cause that's all I had at the time - literally nearly killed me how heavy it was and I snapped the strap on it. You travelling by car? I was by train!