Re cleaning, I used to like to do a big clean all in one go but since becoming a working single parent I now split it up and do small jobs every day so I can try and keep the weekend for doing nice things (whether that be trips out or spending proper time with DD at home).
While DD (4) is in the bath, I clean the bathroom, hang laundry up, put clean clothes away etc.
Empty the dishwasher while waiting for the kettle to boil in the morning. All clearing up done as we go. I do washing up while DD eats pudding.
I occasionally spend an evening batch cooking so that I know there's stuff in the freezer for days when I don't have time to cook.
I get DD to help with dusting, sweeping the floor etc. while I do other jobs in the same room. That way we're spending time together rather than me feeling crap that we've not seen each other much and now I'm ignoring her while I clean.
DD responsible for putting dirty clothes in laundry and folding unscathed clothes to be worn another day.
I have to say though, if you can possibly afford it, I'd get a cleaner! And someone to do the ironing (Having said that, I just don't bother most of the time).
Re shopping, I know you don't want to, but shopping online is hugely convenient and efficient and saves a chore.