You are not alone. I have 3 kids very close in age too, they are girl/3, girl almost 5, & boy/6, so 3 kids in 3 yrs. It is always chaos. Someone is always fighting, crying, hungry, all talk to me at once which leads to screaming then hitting, spilling juice, calling names, into something, etc. My middle one is a whiner & has the same voice as Fran Drescher from The Nanny.
So I don't have a schedule, well I tried but doesn't work for us. So I have a list on the fridge of fun things to do. I always have a bag packed & ready in the van with extra change of clothes, shoes, bathing suits, sunscreen, towels, pool toys & a portable potty!!! These items always stay in my van. Then in the morning I make PB & J, water bottles, snacks & we leave. Most of the time we don't have a plan but we can figure that out while we are in the car. On the days we don't have anything going on they play outside & I constantly give them popscicles & fill up the little pool. They also love to finger paint, outside only, then it leads to body paint. So I give all of them bowls with different colors of crayola washable paints & some paint brushes & paper & they have tons of fun painting on the paper then they start painting eachother. It is hilarious they paint eachothers entire bodies. The only thing to watch for is when the paint starts to dry it pinches the skin a little, it takes a long time for that to happen but it's kind of funny when they don't know what the heck is happening. By then I put a bucket of water with a little soap & 3 wash clothes so they can clean eachother up.
I also suggest trying some playdates at least once a week. But going to parks is equally as effective for some social interaction. We have lots of parks by us that have water pads so the kids can run thru them to release some energy.
Housework is very hard to get to. The only thing that works for me is to clean my butt off at night or put a movie in & hope they sit thru it. We finished our basement for their playroom which helped me to clean. I also use paper plates quite a bit. I do laundry everyday to keep the piles down. I literally don't sit at all when we are home all I do is clean & keep up with the house. So I am trying to let things go a bit more for my sanity& my kids since I am on top of them every minute of the day.
I can say now that my youngest is 3 things are getting a bit easier for me to get things done & to up & go since she doesn't take naps anymore, although she needs them sometimes. So hang in there, next summer will be easier!