I like the design. You have thought about how life should be and make confident decisions, such as the main entrance through the garage. Something unique has been created.
Gallery:
Those who love the feeling of high rooms will cope well with the limitations. Since you have the children's rooms directly adjacent to the upper gallery corridor, you will sometimes have to be more considerate with guests at the dining table than with a closed ceiling. The room acoustics can be managed well – I have the best experience with the LignoTrend acoustic ceiling, and others can surely also report. The gallery is a highlight of the house.
Garage:
That I myself would separate the garage from the house as proposed by – and actually prefer a carport… that doesn’t matter.
If the garage is to serve for 2 cars, children's vehicles, and the main entrance, it is far too small. Do you already have such a double garage in use? We had it that way in our terraced housing estate for over 18 years and only 2 children. Only one family with children parked their 2 cars in the garage, as the rest was used by children and stuff. That family had a bicycle shed in front of the door.
From my point of view, you make the living room too narrow in order to build a garage that does not correspond to the intended function. If that were the case, it would be a "lose-lose situation."