So she opened an item not as described case with eBay? Before the item arrived? Then told you that she hadn't authorised the purchase?
You need to call eBay and say that she had no case for an item not as described, as your tracking prove she opened the case before the item arrived.
If she is claiming that the order / payment was unauthorised, she has to raise a chargeback with PayPal, NOT eBay. If she does this, as long as you can upload the tracking details which show the item as delivered, you won't have to refund.
Don't run about offering to pick prams up and refund.
You need to call eBay and speak to someone and make sure that they understand this, if you don't have any luck, keep trying until you get someone who does.
"The buyer says the payment was unauthorised, this isn't covered by the not as described case that she has opened. In fact it's impossible that she could have decided the Pram was misdescribed, as she opened the case before it arrives, as proved by the tracking and the case date.
Please close this case in my favour, because the buyers issue is that the payment was unauthorised, not that the item was misdescribed.
If the buyer insists the payment was misdescribed, she should open a chargeback with PayPal, not a case with eBay"
Hope this helps.