I agree, you sound great. I am glad you are having success in your sitch.
In this case, I think you are overthinking things and in doing so, you are not hearing your W.
Two weeks alone with three kids and you are treating her to a day off? Look, it is so disproportionate, while the relief is no doubt welcome, the offer of it is going to needle her feelings of resentment, if you know what I mean.
I cannot even imagine how hard it would be to parent three kids alone for two weeks when they are small children. When she says, ""the kids are cranky and I haven't slept," listen to her.
She is exhausted, she is spent, she is emotionally and physically tapped out. At that point, your sexual playfulness just seems like one more demand on HER. She is at the point where interaction that requires giving on her part is simply too draining.
How can you help her out? Can you read or sing to the kids over the phone and let her relax on the couch for twenty minutes? Can you arrange for someone to come help her? Can you hire a maid service? Can you pay for home cooked meals to be delivered to the house? Can you surprise her by having a masseuse come give her an in-house massage?
W needs some relief. W needs to have someone meet her needs. She needs her emotional and physical resources restored. It would be great, for instance, if you could give her a four-day weekend totally off where she gets to travel and have a complete break.
As for sexual playfulness during travel, maybe there is a way to make that restorative rather than draining for her. Maybe try getting her rocks off remotely to help her sleep after a long day, making it very clear that reciprocation is not even on the table?
Anyway, just a few thoughts. The main thing is: hear her exhaustion and don't personalize it.