"A man came home from work and found his 5 children outside, still in their pyjamas, playing in the mud, with empty food boxes and wrappers strewn around garden, The door of his wife's car was open, as was the front door to the house and no sign of the dog.
Walking in the door, he found ...an even bigger mess. A lamp had been knocked over, the throw rug was against one wall. In the front room the TV was on loudly with the cartoon channel, the family room was strewn with toys and various items of clothing. In the kitchen, dishes filled the sink, breakfast food was spilled on the counter, the fridge door was open wide, dog food was spilled on the floor, a broken glass lay under the table, and a small pile of sand was spread by the back door.
He quickly headed up the stairs, stepping over toys and more piles of clothes, looking for his wife. He was worried she might be ill, or that something serious had happened. He was met with a small trickle of water as it made its way out the bathroom door. As he peered inside he found wet towels, scummy soap and more toys strewn over the floor. Miles of toilet paper lay in a heap and toothpaste had been smeared over the mirror and walls. As he rushed to the bedroom, he found his wife still curled up in the bed in her pyjamas, reading a novel...
She looked up at him, smiled and asked how his day went. He looked at her bewildered and asked, 'What happened here today?' She again smiled and answered, 'You know every day when you come home from work and you ask me what in the world do I do all day?...
' 'Yes," was his incredulous reply..
She answered, 'Well, today I didn't do it.'"
When I'm at work no tidying or washing or cleaning happens at all, whereas on mat leave they did get done, albeit very slowly. My children spent a lot of time playing in washing baskets etc. You already have 2 people on your back telling you you're not 'doing enough'. Don't do it to yourself too.
Potential issue with the babysitting: it relies on your DH's support. Is there any risk he might sabotage it by unexpectedly being kept late at work, on days you are working? It's a horrible suggestion, I may be doing him a huge injustice, but you have said he plays "my job is better than your job".
I do think that if the study is essential, you have to drop something else or get some daytime childcare, or find some other solution.