I think this thread has splintered into two separate discussions, with some posters arguing at cross-purposes to each other. There are two issues here - first, whether student children should be obliged to take a job in the holidays, as opposed to "recharging their batteries" by doing nothing and secondly, whether parents should expect/accept a financial contribution to the household from their wages.
Is there anyone on this thread who would honestly defend the right of an able-bodied nineteen or twenty-year-old to spend the entire twelve or thirteen weeks of the long
university summer holiday sitting about at home in an aimless and completely unproductive manner? (Fair enough to take a couple of weeks off at Easter and Christmas.)
This would be totally detrimental to the young person in the sense of turning their back on the chance for new experiences, opportunities and the increased self confidence that comes with them as well as encouraging completely undesirable and habits and attitudes.
Whether parents expect or need a financial contribution from their child's wages during the holidays is a separate matter, with no "rules" and and will vary from family to family. Some affluent families may not need or wish for any direct contribution to household expenses and continue to provide bed and board while simply making their child responsible for all personal, non-essential expenses while they are working. Others may take nothing on the expectation that their child saves at least some of their wages for future use. Other, less affluent families , like the OP's, who are only just coping with supporting themselves, and who incur extra expenses when student children return, are definitely justified in a expecting a contribution to offset this because it is needed.
Therefore, all students should work in the long thirteen-week holiday and those whose families need it, should make a financial contribution.