I also have a big crazy household - 3 kids, 2 cats, 2 dogs, DH and I. I know where you are coming from

My mom is an agent and we have flipped our way up on several houses.
Here are our tricks to sell a home we live in-
1- Destash - trash, donate, garage sale (BUT if it doesn't sell YOU CAN NOT KEEP IT! donate.) Anything that you haven't used in 6 months to a year you should consider letting go of. This includes the kids toys - get them on board with you. IE if they donate toys they are helping kids AND as a reward you will do X for them.
Doing this now, it actually feels really good to get rid of stuff!
2- Curb appeal. NOW before you list work on making sure the outside of your house looks nice. IE you want to get that look where people drive by and think "oh what a nice house." so when you do list you get "oh my that nice house is for sale! Wow lets go see it." Believe me it works! I have seen neighbours by someones house on more then one occasion because they knew the house ahead of time.
RIght Now everything is blooming so I need to get the pix done! Also bought hanging plants for the porch.
3- Empty - rent a storage locker if you have to. You want your place to look bigger then it is. (Even if it is big already!) Take nearly everything out of your attic, garage, closents and storage areas to make the house look like it has lots of storage! Storage areas are great in a home but they detract if they are packed to the gills. Keep a few things in there so people don't automatically think "oh they got rid of everything to sell - they must not have enough storage"
We have 2 storage sheds, just have to get them cleared out so we can fill them with totes!!
4- Define. Do you have any wierd rooms in your house? A bedroom used as a gym, a diningroom used as an office? Time to give those up. Rooms should be what they are - bedrooms should have beds in them. Bedrooms sell better then offices, dens, etc. Same goes for any other places you have had creative planning for. Many people need to be shown what a room is for or they get confused.
Our front room, originally the living room, has 2 computer desks, a futon and a giant fish tank in it. I work at home as a medical transcriptionist and like being in the front of the house so I can keep track of what is going on (I have a son with autism). Can't really redefine, hope people have an imagination? LOL We have a big family room now also.
5- Furniture and paint. Stupid as it sounds since they aren't buying the furniture a lot of people can't see past the decorations to get to the "bones of a house" (This is where I am fortunate because I can and have scored some great houses because of this

You want to make sure that each room is tidy and has nice minimal furniture. Overcrowded rooms don't sell, neither do old dated rooms. Paint out ONLY any odd colours - NO your entire house does not have to be neutral as long as it is tasteful. Don't waste your money or time painting everything just what needs it!
My DH is the painter....he will be home for the summer (he is a teacher) so I'm saving that job for him!!
6- Now I am guessing that renos are out of the question? If you decide to spend any money fixing up the house - first go for anything major - IE do you need a new furnace, appliances, worn out flooring, THEN if you have money go for the big things - new kitchens and updated bathrooms sell. BUT old clean kitchens and bathrooms sell too so if you can't afford the update work with what you have!
We have renovated a lot already, new kitchen, new master bath, lots of new flooring. There are a few things that need to be touched up. The realtor is having someone come fix my kitchen ceiling where Ivan's wrath still is apparent.
7- Get kids on board for open houses. Yes it is HARD to keep your house show room clean but it is easier if you have done all the prep work I have suggested. (Most of which won't cost very much money either!) Make it a game - we play "mess police" we also let our kids help with reno work so they feel attached to the idea of trying to sell. Our older two have been painting and landscaping since preschool. Get them on board that you are going to be living closer to Daddy!!!
Kids are excited to be moving, oldest wants to go to UCF, 15yo wants a fresh start. Littlest wants daddy back. My 19yo son says he is staying here...we will see. Trying to get him to clean his room, I told him Monday I will go in there with a bulldozer - he has been warned!
Anyway I sure hope this helps! Good luck with selling