Regarding the stability problems....if a rider doesn't have experience at faster speeds on a specific type of bike, they may have trouble controlling it at first, but will usually learn to do so over a few dozen miles / days of riding, depending on the rider.
Could also be a hardware issue: if the bike is brand new, it may not be assembled or setup correctly yet. A bike shop should be able to take care of that.
If it's used, it could have any kind of adjustment problem or damage including bent frame or wheels that do what you see.
It could even just be built using a bike with geometry designed for slower speeds than what it's being used at. (even if it's an OEM electric bike it's likely they are using a bike frame/etc that already existed, rather than designed and built from scratch for them).
The first two can be fixed by adjustment or repair / replacement of problem parts.
The last might be fixable by changing parts to correct the geometry for faster speeds, or sometimes by adding dampers to the steering, etc.