Maybe she's just afraid things like this picture would happen. http://www.brainjet.com/random/9769/27-reasons-dads-should-never-be-left-alone-with-their-kids#page=1 Okay. Let's be serious here. If she is satisfied that you can look after your daughter alone, I'm sure you won't need to convince her at all. Show her that you can do it by taking over diaper, milk and bath duty for an entire day without her help at all. Start small. Instead of asking for an entire day, start with a few hours. Buy her a spa session and take care of the kid while she's away.
I agree with Jamie. Start with something small. She'll probably watch you like a hawk and once you know you're ready to move on to bigger baby duty once she asks you to help without you asking. I never trusted my ex husband alone with baby (until now). Mainly because he doesn't listen to instructions and ends up screwing up and then I'd have to redo it plus clean his mess. Listen to your wife - she too probably have her own way of doing it and it is important that you follow accordingly.
When your wife is around in the house, try to learn as much as possible from her, diaper changing, milk feeding, bathing and etc. With her presence, try to practice in front of her with the baby. I believe if you are feeling confident in handling baby, your wife will sense it too. You can start with taking care of baby alone for short hours first instead of whole day.
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thanks