American National made a Packard pedal car similar to your mother's. In fact, that diamond shaped plate near the top of the front grille is the badge shape used for Toledo Blue Streak pedal cars. Toledo being part of American National. Check the ads out on the top right of this Pinterest page:
https://www.pinterest.com/pedalcarspa/pedal-car-literature-ads/?lp=true
Most of the Packard's I've seen have solid wheels, so perhaps the wire spoke wheels on your mother's pedal car were an upgrade option, with solid wheels being standard.
Dave