Debbie, can you remind me again when/where you're going? I've been to Italy in March and it can be very cold and wet- similar to the UK, really. I think Angie's given you a great list, and I especially back a trench, great jeans (they'll be what you wear the most- just wait!), a versatile dress (don't forget the tights/leggings to wear with it!) and scarves.
As for not wanting to leave your daughter, I totally understand. I'm not a mum, but I have one, and every time she has to say goodbye to me at the airport (I've lived abroad for 3+ years) she cries. Every time, without fail- but she says that as soon as I'm out of sight, she's fine. It's just the goodbye that gets her! Remember that this is going to be an INCREDIBLE experience for your daughter, and will likely bring you two even closer in the end (I appreciate my Mum more, now that I get limited time with her). In fact, I'm completely jealous of your daughter- Italy is one of my favourite places on earth!