Based on over a decade of hosting APs, I disagree that hosting APs is akin to buying "Value City" furniture.
One does need to match carefully and work with each AP as if she were the first, in order to acclimate, train, and develop a relationship. I also spend time helping them find ESL and other classes, recreational facilities, know where APs who arrived with them live (& how to get there). A little handholding goes a long way to getting them off to a good start. That takes an investment of time each and every year, and I know some families tire of that. And occasionally, it doesn't work out and you have to send somebody home or into rematch. But in my experience, the APs have almost always been responsible, good drivers, outgoing, friendly and open. In all cases, they have developed good relationships with my kids, way beyond keeping them alive and driving them around. In twelve years, I have never had to miss a day of work due to an AP's illness or an AP being AWOL when she was scheduled to care for my children. And several of the APs did have 2-3 years of child care experience and/or education. Regarding driving, I look for no less than 2 years of daily driving experience, preferably in a climate similar to ours (i.e. ice/snow in winter). And while getting the state driver's license is necessary, their actual driving privileges are based on both skills and where we are comfortable having our car (i.e. any weekend trips need to be preapproved,etc). Although I do not look for party girls, on a couple of occasions, an AP who won't even talk to her host family is a red flag: homesick or possibly lied about something on her application (boyfriend, smoking, etc). Good communicators don't let language barriers stand in the way of getting to know their host family/making friends.
My suggestions, if you decide to try to salvage your current situation:
-- get your AP connected with other Italian speaking APs in your area. If there are none (Italians are not as common as other Europeans in the program), you'll have to be a little more creative. If she speaks/understands Spanish, try connecting her with South American APs. This may seem counterintuitive given that her English is poor, but it is very stressful to not be able to really talk to anyone since she arrived.
-- assign her to care for one of your children for half a day (sole charge, but with instructions to ask for help from the nanny if necessary), then for the whole day, then gradually have her be responsible for all of them. Check in with her yourself a couple of times a day. The first week I am working with a new AP in my home, I call her every day in case there are any questions.
-- take her driving every day, to places that she will need to drive your children to or that she will want to go to (Starbucks, the library, the gym, the mall, homes with other APs). Let her navigate her way once you have done this a couple of times. You can impose any driving restrictions you deem necessary but be mindful of the limits of any public transportation in your area.
--It sounds like your children are predisposed to adjusting to new, youngish caregivers, so that should be helpful. Be sure the AP has time to be with your kids without you or the nanny getting in their face.
If this doesn't help, ask for a new AP ASAP and send this one home. This is important to ensure you have someone viable in place before the nanny leaves.