It is hard to keep a house in good order to maximize it's appeal to buyers, while it is on the market, and even more challenging with some lively kids!
Homes do show better if they are "staged" like a model home. This even works with your own furnishings, although you may want to have another person help you with deciding on the best arrangement, what to keep in the house and what to store elsewhere. HGTV's "Designed To Sell" is all about making a house look great before putting it on the market to sell....and get the best price!
Tari is right about cleaning, the cleaner the better, one more reason it's harder with kids. Kids need more freedom to play and be...well, kids than having to keep everything "perfect"!
It's great to have the option of moving in temporarily with your parents, but be sure to understand that your house could be on the market for a couple of months before getting an offer. Can you, your kids and parents cope with that? That is something else to consider.
You may want to compromise and move out for the first month (when you get the most traffic) , take a week to clean and arrange your furnishings (remember to store extra stuff) then put your house on the market. After a few weeks and strategizing with your agent about when and if you might move back,. One reason would be that you have a mutually accepted offer, and 30 days to close.
Good luck, and best wishes on getting a good offer quickley!