You've gotten a lot of wonderful advice already. Your place is really cute and I'm sure you'll find a way to make it work for your family.
In the kitchen, get in there and really get them organized and put things away, and add an extra shelf if needed to really get things put up. We didn't have any pantry space so I brought in a bookshelf and used that for my food storage. Here's a picture.
(I'd suggest one with doors for a less cluttered look. Maybe the IKEA Billy cabinet?) It would fit nicely at the end of your island, where the paper towel holder is currently. Your kitchen looks like it has plenty of storage if it's well utilized. Maybe you could take pictures of your open cabinets so we can see what you have and what needs to be put away in there?
I loved the suggestion of a corner booth style dining table and seating. It would add needed storage and clean up the look of that corner. We have a booster seat that attatches to the dining chair and we've used that since DS was 6 months old. That may be something to consider to get the high chair out of the way.
The sofa is really pretty, but awfully big for the space. Maybe something like this
would work a little better, since it is smaller but still gives space for seating. It also has storage under the chaise which could be used for blankets, and it's a sofa bed. The space freed up next to the sofa could be used for musical instruments. A storage trunk like this
would make a nice coffee table and add storage. (There is a matching trunk end table. Even more storage!)
Your entryway is outta control! How about something like thistwo door/1 drawer
cabinet that could be used for shoe and bag storage underneath and keys and such in the drawer, with hooks hanging over it for coats.
Of course, you don't have to buy anything to get the place cleaned up, but perhaps furniture that was scaled more suited for the space and had built-in storage would give you more room to work with help you (and your family) keep the space tidier.