I'm not a SAHM, but my friends who are have expressed the same frustrations. To be candid... as a working mom, I was able to keep up on household things by staying up late, getting up at the crack of dawn to exercise and spending my weekends "catching up" during naps. It wasn't fun.
So... I won't lie... we hired a housekeeper. I wouldn't have done it if I wasn't working full time and commuting an hour each way each day. The ONLY thing I have heard from my friends that "works" is to have a weekly cleaning schedule. Mondays are always bathroom scrubbing, Tuesdays are deep cleaning the floors, Wednesdays are the kitchen, etc. Children who are old enough to go to school are old enough to put their own clothing away!
If you were working outside of your home, you would schedule things into your day so that they get completed. I have one girlfriend who is a great SAHM to two boys, a husband and a dog. She looks at her day just like she did when she was working in the corporate world... what needs to get done this week? Then schedule your day accordingly.
As for the toy explosion- the preschooler is old enough to put them away when he's finished. We have a "rule" in our house... if you are taking something new out, put something else away. He needs reminders, but my house doesn't look like a war zone at the end of the day.
You're not missing anything- we're all always behind, but at the end of the day if everyone is clean, fed, clothes are clean for the next day and lunches are packed AND I have time to actually talk with my husband, we consider it a successful day in our house!