My Dog Won't Stop Vomiting

We've had Fiona for about 5-6 weeks now. We love her. She's so cute and funny and always learning new things. In her quest to discover everything, she's taking up eating things in the yard (leaves, sticks, mulch, grass, mud, etc.) Because of this she barfs all over the house. Sometimes she just coughs up barf and swallows it back down before it hits the floor, sometimes she projectiles all over everything. She's barfed in the bed twice now, in the middle of the night, mid-sleep. I've talked to the vet about this and have even had her in for the vet to look at. His thoughts...training training, training. So now we have to take her out on a leash EVERY time she goes out and snap the leash when she gets into something naughty...which is all the time :( I feel bad for her, but I'll be glad when she doesn't barf all over.