Hi Jude,
You were acting by the letter of the law to ask for a PCR, as you know Lateral Flow is for when you have no symptoms. It looks like you daughter may have reacted to not having child care and may well need to get a more formal arrangement however there will be many twists and turns for her and she may well need to come back to you anyway to help as places and days are not guaranteed. In the mean time perhaps pay to go out to coffee / lunch somewhere neutral with her and ask her how shes feeling? See what comes out and gently explain that COVID is life threatening for your husband which is why you were concerned. If she still remains unreasonable then you may have to sit back and be supportive from afar with calls and small gifts, there may be more going on that you know.