A, You really are assuming way too much these days. First, you don't know your h while he's in crisis. They become someone totally different (mirror image). Second, the MOW may not be pushing him to do anything, this may be all him. Third, you are giving the MOW far too much credit for the things that your h is doing while in crisis. Fourth, he may have spent time in hotel/motel rooms on those special days because he can't face you and the family, nor face that dreadful room he stays in. He wanted a change of scenery to make himself feel better. Are you even sure she was w/him? Do you have proof? If not, please don't assume anything until you have the proof sitting in front of you in black and white.
Yes, your h is looking around at the yard and everything else that is familiar w/him. He's lost a lot during this time and they have to sit and look at things to be reminded of what they've lost. It's like a child holding on to mom's apron string. It's their last hold on to what was familiar before going full force into the unknown.
You are still expecting him to do certain things. Toss that expectation out the window. How often do we talk about keeping expectations at zero? You can't expect him to do things the way he use to. He's gone, he's lost and he's very depressed. You need to stop expecting him to do things because all it does is disappoint and frustrate you. Expectations at zero and when he does do something nice, be surprised and enjoy those surprises.
You are still giving the MOW far too much of your head space. Let it go, keep the focus on you and your children. You and the children need to let him go totally in order for him to complete his journey. Plan activities around your little family's schedule, not your h's. Pretend his gone to Mars for a while and when he does appear, it's a postcard from ET.
Keep the faith and allow God to work this out. Instead of giving it all to God, you continue to snatch it back for analyzing. There is no rhyme or reason for what he's doing or thinking because he's depressed and depressed people do not think or react to things the way normal, functional people do.
Have you done any additional reading on depression? You should. The answers are all there...describing his behavior, etc.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.