I think the Tuesday night thing is good. Show all of them you are fine and ok with doing this. Its for your girls and what is best for them.
As far as the gift, I would get something for her from the girls. Something small, not extravagent and something they would give her.
How are you doing on not responding quickly? I am doing decent..not great all the time. Saturday morning exh texted early to let him know when she was awake so he could come over. I didn't respond. He sent again. I didn't respond. Then he sent "What the F***?" I waited another hour and he was clearly mad that I didn't answer right away.
Me: 46 FWS: 36 Married and Divorced 4/07, Pregnant 7/07,False R 7/07 Baby Girl born 3/08 Kicked him out because OW: 7/08 5/10 He realized what he had and lost. Moved home! REMARRIED 3/14/11!!