Try batch cooking and have a plan of attack for cleaning and laundry -- a routine. You will feel so much more on top of things if you know the bathroom will be done on Monday, kitchen on Wednesday, etc. You won't feel so much as if you are always chasing your own tail even if it's Saturday and the bathroom is a disaster.
There are little things you can do daily in the busiest areas that will keep you from feeling you are fighting a losing battle -- wiping down all taps and the washbasin and the loo with windolene daily will keep the bathroom from looking encrusted with dirt, keeping your kitchen countertops as clear as possible and keeping your sink from filling up with dishes and cups, etc will give you peace of mind. Deal with all used dishes immediately. Hopefully you have a dishwasher?
Get a freezer and a tumble dryer. They are well worth investing in if you don't have them.
I hated the sheer drudgery of it all and got out of a lot of it by not cooking Every.Single.Day. Freezing batch cooked meals takes a load off your mind. You don't have 'What's for dinner?' hanging over you all day. I always had a dryer and got into a routine of putting on a load, folding and putting it all away daily. I never ironed, just got good at folding. I sent exH's shorts to a dry cleaner. He had two weeks worth and the cost was well worth it even though picking them up again was a pita. They did a far better job than I could have.
Keeping track of toys and general stuff is possible with little ones if you put in about 15 minutes nightly after they have mercifully fallen asleep. But though it's hard, training them to help with this is the best idea in the long run. It can be light hearted and fun -- have a song, a race, set a timer and see who can put the most stuff away, etc. as long as they eventually develop the association with playing being followed by putting away at the end of the day. It can be part of the bedtime routine.
I never had carpets downstairs and went around with a dust mop daily to keep on top of cat fur, hair, general dust -- we have allergies here. Then I damp mopped a few times a week too but I always found that easier and less of a physical effort than hoovering carpets.
There is a difference between unclean and untidy. Aim for clean -- and rope your DH into tackling this. Untidy never hurt anyone, and can easily be remedied daily.