Haha don't go completely open plan. It's attractive with toddlers but as kids get older 1. they go to bed late 2. they watch awful telly and play on video games. You need to shut that (or yourself) away. Also if you have a room you can use as a study, don't give it up lightly.
Personally I would try to keep your hallway open - I can see your bathroom has been sacrificed to stairs. Its a PITA having a house where you have to squeeze past a dining table or some poor sod trying to watch TV every time you want to go upstairs from the main room.
I think you have the layout about right keeping the kitchen where it currently is and dining table in the L. I would block up the door to the old bedroom and re hang the kitchen door to open into the hall. That way you have more space for table and chairs and maybe storage.
With an island/peninsula you have to decide what is more important, sociable congregating or concealing the mess of cooking. If it's the 2nd you could have a split level island with a bar/serve out shelf higher up but a small upstand hiding the worktops.
If you want an area to gather round it would be best if it didnt' block the route to the back door, make it wide and flat so the stool-perchers aren't too close to the hob.
I've found it nice to have a hob on the peninsula, with a big space beside it to prep and serve out. There are ceiling/wall extractor solutions that work espcially if you are rebuilding upstairs. Rather than cram the cooker into that space by the back door. Put storage/dishwasher/larder over that side.