Traveling to US with unvaccinated child

I'm fully vaccinated but my 7 year old is not eligible  Is the following correct?
-We both need a rapid antigen test 3 days before (since she's traveling with me and I'm fully vaxx'd she can take it at the same time instead of waiting for 1 day before travel)
-We both have to take a COVID test on before day 2 of arrival back in the UK (no video superivision required)
-I have to complete a passenger locator form online before we arrive - is that one per person or do I include her on my form?

Second, should I just order both sets of tests at the same time? I was going to use Qured since it's been recommended here.

Third, if we test positive    we have to self-isolate for 10 days - then are we allowed to travel? It's a long trip and in the middle I'm going to a memorial service for my mom so I'm hoping that I can still travel to that.

1) You said this: "since she's traveling with me and I'm fully vaxx'd she can take it at the same time instead of waiting for 1 day before travel". Where have you seen this? The point of the 1 day before travel for unvaccinated is because there is a higher chance of picking up covid. Who you're travelling with has zero influence on that. I'm happy to be proven wrong but it makes no logical sense to me. Without delving too deep I also cannot see it on the CDC website.

2) Correct

3) You can include children on your PLF providing they're staying at the same address.

4) You can order at the same time. They all may come before you travel. Qured is supervised, just so you know.

5) Yes you're allowed to travel. However, you have to get a signed document of recovery from your doctor which exempts you from taking the required travel tests (due to the likelihood of testing positive). But,  this is virtually impossible to get from most GPs. You can take a chance on your lateral flow tests showing up negative in which case you don't need the letter but there's a significant chance this won't be the case.

Make use of the NHS tests prior to taking the travel tests. This will give you a strong indication of what result your travel test will be before you waste it pointlessly. They're all basically identical tests with a different logo on and box.