How do I convince my wife to leave my three month old baby girl with me alone. She is afraid I won’t be able to handle it?

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.