This is a classic example of a particular type of man who conspires to never do 1-1/entertainment with child. He can't be bothered.The DC gets stimulation at school then once that's done, mum has to take over.
Lots of child-free time for him as well as the hobby etc time available to him in the week - meanwhile mum's child-free time is only when she's at work. Leisure time for her isn't a consideration
Laughable that people are saying where can he go/why should he take DD out on Saturdays. You go out there 8.30am onwards and see how many mums are already busily out and about with little ones. Do dads disintegrate if they do say 2 hours park on a Saturday morning..?
You're asking for advice. Ok then. Sit your DH down tell him you are not prepared to work full time + do a significant chunk of housework + attend to DC weekends so that you never ever get a (leisure) moment to yourself and are relentlessly working both inside and outside the home.
Have a rota drawn up, hand it to him. Balance out your time. If he still won't listen - then you'll just have to be upstairs having a lie-in, noise cancelling earphones in, bedroom door shut, curtains drawn. Don't get out of bed. Don't answer any queries such as "do you know where so n so is". If he tries to stay in the bedroom with you tell him no, you want to rest. Be very consistent.
They don't have to be out of the house so that you can have some peace. You just need to be assertive about having that peace.
Go on Amazon buy the earphones it won't take long.