I wouldn't tell your employer, at least nit in the way you seem to be going about it.
The bottom line, from their POV, is that come September, even DC from shielded families can go to school and return to the household where the (by then de-shielded) person lives, even if it is difficult/impossible to keep any form of distance within the household.
As that is household proximity with someone considerable more vulnerable that than the classification for the elderly, there is no way that the situation with the grandparents will be seen as anything other than disinclination, going beyond the official advice.
So raise you request in terms of working flexibly being good in its own right. Can you demonstrate that you have been more productive? Can you show they can have a more Covid safe workplace if fewer staff are in on a regular basis? Can you show how the business is more resilient, in the case of eg local lockdown or Test and Trace required isolation, if they have some staff established as WFM?
Also you could make it a formal flexible working request, of the sort you could have made before Covid, and with considerable stronger evidence that it is positive for the business?
You need to show then whats in it for them, not talk about childcare issues.
And then you will gain the flexibility you want to arrange your wider family's infection control measures as you wish, including going further than the government advice if that is what you think you need