Wow I understand this so well. With our oldest (17 yo) in the house it is mear impossible. any little thing that she isn't meant to hear - she has sudden bionic capabilities - anytime day or night.
A few things we have done.in ( you may not have the flexibility work schedules but will list all just in case something works for you) Moved bedtimes up 30 mins and stuck to it - creating just a little more room. rise before the children by at least 1 hour at least 2 / 3 days per week and on weekends. During the terrible period of the first 6 months after discovery we would 'walk' for excercise and end up sitting on the oval talking through issues.
Commuting together if possible. (our commute is an hour)
Meet for lunch / work from home on the same day. (but our children are school age).
Once we had DS with us who is younger, we went to ikea booked him into kids playroom for an hour and sat down together to talk.
We early took some close trusted friends into our confidence and they would have DS (in particular) for a play date while we talked.
it is so hard to work through disclosure, healing and reconciliation with children in the house. In ther early days ours saw way too much too! We sat with them and answered their questions as honestly and age appropriately as possible. Reassuring them that although we were in a difficult time we were determined to heal our family, to get stronger and be together. This relieved a lot of anxiety of the unknown for them.
Depending on age of your children - some more open and reassuring conversations with them may help them to feel more secure. It helped for ours.