Yes, using the wider angle of your Vivitar might have prevented some of the hotspots but, I am not at all a fan of the hotshoe Strobist doctrine!
Using a shoot through umbrella or softbox to diffuse the light that has been concentrated by the relatively tiny flash-head of any hotshoe flash is a lot like boiling ice cubes to make tea. It can be done but, it sure as heck is not the most efficient way to work.
A studio strobe will have a far larger reflector than the hotshoe flash, so you are starting out with a larger light source to begin with. A studio strobe with a reflector 6" in diameter will have a reflecting area of over 28 square inches. I don't have a Vivitar handy to measure but, my 550EX has a reflector 1.5 x 3 inches; providing a reflecting area of 4.5 inches or a very small percentage of the area of the studio strobe's reflecting surface. Additionally, the studio strobe will usually be positioned shoot almost directly into the center of an umbrella, where the hotshoe flash, since it needs an extra accessory mount to be used with an umbrella, will normally shoot through the top half of the umbrella - causing less than even lighting.
However, the primary advantage of a true studio flash is the modeling light providing "what you see is what you get lighting. The hotspots on forehead and cheeks could very well have been detected when viewing the subject with the modeling light.
I don't know how far your shoot-through umbrella was placed from your subject or how far from the umbrella the flash was placed but, both these variables have an impact on the softness of the lighting. The closer the umbrella is to the subject, the softer the light will be. The impact of the flash to umbrella distance is pretty well dependant on the size of your flash reflector. Tiny reflectors used on hotshoe flashes will not cover a large umbrella evenly.
However, that all said, the proper use of makeup will often prevent the shine causing hotspots. Few females, except those who have done some modeling are aware of how to apply makeup for photography. Do a Google search using "photographic makeup" as your search parameters. That will provide links to various sites recommending the proper application of makeup for photography.