LOL - what cleaning routine??
I am a SAHM of a 2 year old, a 6mo old puppy, and a husband...my priorities are floors because puppy drags in EVERYTHING and I watch two other toddlers a couple days a week, so most of my efforts are put into floors. Other than that, I do what I can when I can. Kitchen counters are probably a 2nd priority for sanitary purposes, but it seems as soon as I get them cleared and cleaned, it is a mess again! Like you said!
My standards are high when it comes to cleaning, but something is better than nothing - for example, one night my husband just sat down and folded towels (I think he was ill!! or drunk!!) and he kept asking "how do you fold these?" and I would tell him, but it still wasn't "right". Instead of saying anything or letting it bother me, I took it for what it was worth - a chance to have something get done and not have to worry about it myself! Give your kids the jobs that don't matter if they are done right - dusting, picking up, mirrors, folding socks, etc. whatever are your "negotiables". Then save the "non-negotiable" jobs (in my house, the floors, sinks, bathrooms, etc.) and get them done whenever you have a chance.
One day my husband came home to a messy house and asked what I did that day...I told him I was a Stay at home MOM not a Stay at home MAID!! That shut him up real quick... :-D I have a sign that says "Please pardon the noise and the mess, the kids are making happy memories"...I used to have it hanging outside my classroom when I was a teacher...I think I should haul it back out and hang it somewhere in the house! :-D