Yes, you can. Parking is limited, so do yourselves a favor and carpool please! It is a 15 minute drive from the ceremony site to the reception - you can leave your cars overnight in the reception site parking lot (if needed).
No there is not Uber in Mammoth. But, for all you trying to really let your hair down (which, we hope you do!), there is a local taxi service 760-934-8294, Mammoth Taxi.
Mammoth Mountain Inn is closest to the reception site. All you have to do is take the gondola down from the reception site and you're at the hotel! It's also the most cost friendly. Village Lodge is in the village of mammoth, located close to restaurants and bars. Juniper Springs is great for families and having somewhere quiet to stay.