My latest theory is that CW hadn't planned this murder out beforehand. (The deleting of the SM a week before is very suspicious, however.)
I think the girls were alive and asleep when SW got home.
I think SW's suspicions of CW's infidelity became confirmed when she got back from NC. Perhaps a friend mentioned seeing CW with a woman, or someone mentioned seeing a woman enter the house while she was gone. Or maybe SW came across some evidence of the affair at the home.
SW may have ripped the sheets off the bed when she learned that his lover had slept in the bed.
SW was going to sleep on the couch that night. CW was not happy. They got into a fight (an "emotional discussion," if you will). It got physical, and loud. The children started to wake. He put his hands on her throat and started squeezing. The rage filled inside of him. She struggled and thrashed, he held on tight, and one or both of the kids walked in and saw this. SW went limp, and the kids started screaming.
What was he to do? His daughters just saw their father kill their mother. They were screaming, the dog was howling. The neighbors will hear! He puts his hand over his daughter's mouth to stop the screaming, and it only worked if he cut her air off entirely. Eventually, she went limp, too, and it was on to the other daughter.
Then he went into panic mode, cleaned up the mess as best as he could. Locked the dog in the garage while he figured out what to do with the bodies.
I would say he would have better odds convincing the children that they didn't see what they saw vs. what you are saying. IMO.