Another eBay postage one

[Coronacantcope]

I need perspective.

Sold an item, the buyer doesn't live near me but lives near my family member who does my childcare so I got her to deliver it.

Should I refund postage? The buyer is incredibly rude (emailed me within half an hour of receiving the item to say I should refund her postage or else send her some more items at no extra charge since I have saved postage and has been emailing twice a day since) and I am so riled I can't be objective.

Well you didn’t post it so yes. I thought it’s against ebays t&cs to make profit off postage and packaging.
Did you drive to meet this person? Did you package it up? If so be fair and take that into account.
But yes you need to refund the rest

I wouldn't. Explain to the buyer that you used a courier.

If the buyer was that bothered by postage cost then they could have picked it up themselves.

You delivered it. You could have paid your childcare person to do it. Don't refund. Ignore and block.