We decided to propose you a young and fresh design, modern yet cozy, playing with light blue and purple colors.
For the kitchen we suggest to add some wood finishing to the style chosen in order to give a warm touch to the white.
For the floor we would suggest to use laminate wood, there are many coded with AC5 that are suitable for high traffic and also water resistant so you can put it in the kitchen too, in this way you don't have to operate any division in flooring. On the market you can find cheap yet good quality laminate (for example at Leroy Merlin). I myself have laminate wood in my house from Leroy Merlin and I'm very satisfied with it, also it's the best for heat at sol, because it keeps the warmth, while tiles get colder.
At the wall next to the kitchen there is space for a big wardrobe you can use to put many things. We used dark doors to give an elegant touch to the ambience, for an original idea you could use blackboard doors (Ikea) so you and the boys could use them to leave messages and reminders to the rest of the family.
As for the bookshelves we gave you an idea of the design you could use. Those brands are probably a little expensive but you could contact a local carpenter and have them made of the dimension you want for way cheaper.