hmmm, since I don't have kids in the house anymore except when the grandkids are here I don't deal with stains really. But I do know hair spray will get ink out of things- spray it before washing.
I don't have too many tips on speed cleaning but I do have little things I do to help. I will spray the bathroom down and leave it while I go do something else like dishes and let it soak- less scrubbing that way. I do use alka seltzer as toliet cleaner sometimes too- toss a couple in and let it fizz. Or I put bleach in the bowl, let it sit and it pretty much cleans itsself. I use micro fiber towels to clean windows and mirrors- no streaks.
When it's nice out and I plan on hanging laundry out to dry I will do it while I am working so it's done and ready to hang when I am done working. I start the first load right before I start working then run to change loads quick. Then when I'm done working the laundry is in baskets and ready to take outside. When I bring it in, I fold it as I take it down so it is all ready to be put away when I get inside.
If I don't have time to really clean, I will put things in baskets so they are out of the way and not so noticeable. I used to do that when my boys were young- kept a few baskets around and if I had to pick up quick I'd just toss their toys into the baskets, books in one, magazines in one, etc - - the stuff might still be right there but it's not spread all over the room.
I'm not sure if any of that will be helpful to you, Kriss but I don't really have tricks- I just try to do more than one thing at a time so I get done sooner. lol