I understand that but let's put it into a bit more perspective. Let's say OP could not afford someone to come in and clean but she was demanding it anyway would he still be TA? Nothing has changed with the exception of what he could afford as it's his money that they would be spending. She's contributing in labor not in monetary value which while labor is worth money, it doesn't bring in money from nowhere.
How much money is her labor actually worth? Could you put a dollar figure on it? I know I couldn't. I share expenses with my wife because she also has a job not to mention we share household chores and other things like bills and such. Whatever I bring into the household is ours, yes, but ultimately it's my money to be using. If I didn't feel it was fair of me to pay for a maid to come in and clean my house then I'm not going to do it.
Keeping up with kids and housework is tough fucking work I know and it lasts until those kids go to bed but to pawn work off on someone else seems a little ridiculous. OP has already made it clear he helps with some chores after he's done work so is he expected to pick up 50% of the slack after he's done work? Guy comes home from an 8 hour job plus travel time and has to do 50% of the household work on top of that? I sure wish I could pawn half my work on someone at my job. If I was at work and had additional work inside of the building on top of my regular job then I would do it, that comes with the territory of having a job and you agreed to it when you signed up for it.
However, I do feel like house cleaning is part of the job being a stay at home parent. I do cook 75% of the time, since I enjoy it and generally know how to cook a wider range of foods. With that I generally do dishes and keep the kitchen clean. She does do laundry 90%.
So OP does yardwork as he said before, he cooks most of the time, keeps the kitchen clean and does laundry sometimes as well on top of his job. What else could she want from him? Nobody deep cleans a house every day so an argument about her cleaning every room every day is out the window, what realistically could she have to do on top of having the kids for the day? Laundry? Cleaning up kids toys? I understand having children is an all day job but calling OP an asshole for not wanting to get a cleaner is ridiculous. If he was contributing nothing besides money then I would 10000000% be on your side but it seems he actually contributes a fair amount of work to the house so I'm inclined to disagree with everyone calling him an asshole.