I think with a two year old and an 8 week old, you have to lower your standards to a point. You work long hours, but your partner is still recovering from giving birth and has a 8 week old and 2 year old to look after with what sounds like very little support from you in the week, so no wonder things have slipped.
One load of washing a day. Set it up the night before on delayed start, then hang out in morning.
Stop ironing.
Order food shop to be delivered online or click and collect.
Get a cleaner if possible. If not possible, have a quick tidy up (like literally set a timer for ten minutes) each day and a cleaning schedule to break stuff up. E.g:
Monday: Clean kitchen.
Tuesday: Dust.
Wednesday: Hoover upstairs.
Thursday: Hoover downstairs.
Friday: Change bedding.
Either clean the bathroom while toddler is in the bath, or do a tiny bit each day, Like clean the sink on Monday while brushing your teeth, bath on Tuesday, toilet on Wednesday, mop floor on Thursday. Use disposable wipes to make life easier for now.
Alternatively one of you run around for a couple of hours on the weekend and get it all done then, but you're both probably too shattered atm, so little and often is probably best bet.