The rules are a separate issue here to common sense.
You can follow the rules. The rules do not affect your risk profile. Understand the difference between rules and risk. They are not the same thing!
You had a household contact. It takes several days to become infected. Engaging your brain would tell you that meant you were at high risk of becoming positive a few days later. Probably whilst at parents. And if that happened you would be at your most infectious.
This is why i despair of people just blindly following these rules and over relying on lateral flowing like crazy in this situation.
Don't see vulnerable family if you have a household positive within 10 days if you can help it! Its that simple.
The experience of schools has been that one child gets it, but siblings are supposed to be in school still. However they tend to get it and manage to pass it on to class mates in the interim between starting daily tests because its one of the most infectious periods.
This led to Public Health England going against the government advice and telling schools which were having large scale outbreaks to send home siblings. A friend at a school which had problems early on and worked closely with PHE said they were advising families to do a pcr 4 days after the first case in the household and not immediately because they tended to first test positive on average 4 days later.
I actually thought this was fairly widely known by this point. Its not been a State secret. There's threads all over MN about it. Once someone in the family gets it, everyone else does tend to go down with it one by one unless you get lucky.
All the lateral flows tell you is you haven't tested positive yet - they don't tell you if you are incubating it and are about to test positive. That's why managing your exposure and number of contacts where you can is advisable.
The inability of people to understand that lateral flows dont 'keep you safe' has always bothered me from the start. People wouldn't see vulnerable family in this situation without them. Its a false sense of security because people think rules are infallible and ltfs are a magic protective force field.
Its like the people who borrowed from Northern Rock who came out with the wisdom 'well they wouldn't have lent it to me if I couldn't afford it' rather than doing their own due diligence and questioning whether it was really a good idea.
Take advice. Follow rules. But also engage brain and don't rely on the State to provide you with infallible advice. It just doesn't work like that. Manage your own risks too.