May 12 is very early for a day trip. Unless everyone in your group is fit AND has alpine climbing experience, this plan sounds bold, to say the least. You should be prepared for non-trivial travel on snow (including navigation above the Outpost camp) and, possibly, icy sections. You will probably need to take the direct (steep) route from the Trail camp to the Trail crest. If this does not scare you, I recommend establishing a firm turn-around time (no later than 2 pm). You don't want to get stuck up high when the snow starts to freeze again, making the descent more challenging. Also getting to the summit late due to slow progress will increase your chances of exhaustion and hypothermia on descent.
Cheers
