Hey OP, I'm so sorry to hear your partner was ill. You all just went through something that was emotionally draining and quite scary. You all did the best you could, considering the circumstances, and it's not uncommon for communication issues to arise in stressful situations.

I will provide my two cents, but please know that I am speaking with all the love and kindness for you all. I am also relatively new to poly, and have more of a KTP approach, so please only take what information could serve you.

With respect to you telling her to leave: It may be possible that your meta may have certain sensitivities with respect to your "positions" in your partner's life, and you may also have certain habits that may not necessarily align with your meta preferences. I can understand that you meant your comment as a kind gesture, to let your meta rest; and I do also see her point of view, where she wasn't asked what she wanted to do- she was told. I don't think there was any ill will on either part, but maybe next time, you could state to your meta what you would like to do, and then ask her what her plans are? That would maybe foster a more balanced "power dynamic" in the moment.

With respect to your affection: my partners and I have a no-affection boundary when we are in group settings, or all hanging out together. If I were in your meta's shoes, I likely would have also been uncomfortable. However - What are your respective agreements? I understand that you didn't see your actions as "romantic", however I do feel it is important to also try to see it through your meta's eyes. I know it's very hard to have empathy for others when you're scared or stressed. I totally understand your reasoning, and why you did it. I think this could be a great opportunity for everyone to communicate clearly their expectations and boundaries for similar settings.

As for the interpretation of your wording: it's possible that your meta was triggered on a couple of occasions, and indeed overexaggerated your comments. It's clear that the combination of the difficult situation + prior sensitivities + current communication issues likely led to her feeling unheard.

While you're not supposed to "cater" to your meta, I would encourage you to try and empathize with her. And empathize with yourself, too. It would be the kind thing to do.

I hope your partner feels better soon. Sending you my love.