I also have a tiny apt and a family of children baruch Hashem.
However, I don’t start Shabbos preps until thursday afternoon.
Preparing all my shabbos food takes about 1-2 hours.
Cleaning takes me another 2-3 hours.
It shouldn’t take you more than that. If it does, then maybe you have to cut down on some cleaning and do things during the week.
You should also freeze any Shabbos food that’s possible to freeze (soups, compote, Challas).
Regarding the mess- every blessed home gets messed up 10 minutes after it’s cleaned! You cannot help that!
And yes, whoever I speak to, including myself, says it takes until MONDAY to get the house back in order. So what? Drop the pressure. Do a little bit at a time.
Hatzlacha!