US here - DD4 was off on June 2 and will go back iirc on 21 or 22 August. There is a break for Thanksgiving (Thursday, Friday plus the last weekend of November) and maybe a day off on Columbus Day (about 10 October iirc) and that is it from August to Christmas. She will have two weeks at Christmas and a week in spring plus a few single Mondays (president's day, Pulaski day, maybe one other).
Just about the same start date for my niece in Dublin but she won't go back until the first week of September.
Wrt childcare for the summer - lots of people around here hire a teenager to take care of children for the summer. Or they hire a teen to drive their children to camp daily (DD3 recently scored a job doing this on top of her late afternoon job in a local day care). Park District camp places are allocated by lottery here because there are fewer places than children. DD2 took care of a neighbour's children 5 days a week as a teen for a summer. I think American parents are less skittish about hiring teens to take care of children than British parents are.
There are lots of privately run camps too. A coding and robotics club opened up a block from me in the spring and it is packed with children daily. There is a gymnastics centre that runs daycamps, a YMCA (both day camp there and sleepaway camp out in the woods somewhere). The local library runs reading programmes - DD4 is currently a volunteer leading little groups in reading-related activities four afternoons a week. Children read a certain number of books and get tokens for prizes.
DD4 is doing summer school all morning for 6 weeks hoping to bump up a level in math.
The local elementary and high school districts operate free summer meals through three local church halls that are spread out throughout the districts, on a 'no questions asked' basis.
Some children go away to camps - I know one child who has gone to traditional camps in the woods and sport camps back to back all summer every summer from age 5. She is currently on a summer course in an English university (now a teen obv).
The public and private high schools and middle schools operate summer camps too, in sports, arts, and drama. You can do virtually any sport. This is for children aged 10/11 to 14.
There are also summer camps for 'highly motivated children' operating in the local small university, with themes like chess, bugs, aerodynamics, Rube Goldberg, robotics, 'Hunger Games; intro to genetics', chemical reactions, 'sudoku and such', physics and engineering, etc. They are basically day camps for children aged 7 to 14. You bring your own lunch and there is a daily swimming session too.
There are two public swimming pools and one year-round rink that occupy children very well from the end of May to the beginning of September (and all year for the rink). It's $50 for a season pass for the pool per person, or $9 for each visit without it. Waivers are available depending on income. Many children 9/10 and up spend most of their waking hours in the water or skating.