1) At that age, my son started helping me with chores.
Yep. They take longer. But it ALSO uses up hours in the day :) Infants/toddlers are the worlds BEST mimics. So if you're wiping down a counter, hand him a damp bar towel, and he'll wipe down the cabinets. If you're cooking give him stuff to stir/ rip/ etc. If you're doing laundry, have him help sort into colors AND have him toss the clothes into the wash.
Will it take 3 hours to do 1 hour's worth of chores? Yup. And in 2 years, it will take half an hour, because he'll have your back and be a serious "helper".
It's also great learning ops. Colors with laundry, counting with dishes, and oh so faaaaaabulous with following directions.
Put the baby to work. :D He'll love it. He's wired to copy you, so don't give him toys that PRETEND to copy you, but actually let him copy.
2) Have a "water baby"? Get a big toy bucket with rope handles, fill it half full of warm water & bubbles, strip him down, plop him in, and drag it room by room with you as you clean. LOVED this trick when mine was small. Sometimes I even just pulled it up by the couch and read a book
3) Babyproof the bathroom... and lock both of you in and take a shower. Have a door stop? (the kind made out of twisted wire) It makes the BEST noise. Don't have a shower connected to the toilet? Show him how to flush it. Give him a few toys and take a shower.
When my son was an infant, I took 2-3 showers a day. If he was awake, I just strapped him in his carseat. Once he was about 1 year old... I just let him play in the bathroom while I took one of my 2 showers a day. One in the morning when I woke after he'd eaten (would also bring the highchair into the bathroom with me... he'd eat while I showered), and one at night.
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It's time for workarounds!!! You can do this.