If I read it correctly your lawyer thinks that the kids sleeping over half the time is too disruptive? If so, time to get a new lawyer.
Everything I researched said that the kids need to spend time (including overnights) with BOTH parents. Google it and read for yourself.
You need the kids to stay with you overnights. Don't settle for anything less. Staying up late curled up on the sofa wathching their favorite movie and then breakfast the next day is priceless time.
Don't keep them and you would send the message you don't want to and are indeed just "visiting". Knowing your stbx that is what she would say.
I get them every Thurs night and every other weekend: Thurs after school until Monday morning when I take them to school. It works fine. If I had a choice I would get them every Wed and Thurs. I keep mine 50% in the summer - basically all June and she gets basically all July. My kids don't "pack up" - clothes at both places.
