Looks like what we've always called "Flowering Almond". Ask at your garden centers or google it. Had one in Ohio which always seemed to get nipped by frost in the spring; now we're in east TN and have one here. It does really well here. Is sending up shoots from extended roots in the ground. If your neighbor's has been in for quite a few years, maybe you could dig up some shoots from the roots if it has any. The one at this house has been in probably 20 years.
We trim it frequently to keep it sized to fit its space.