75-year old new rider needs advice
There are three common causes for erratic steering at low speed. 


A possible cause, but the least likely, is that the head stem is too tight. When not on the bike try turning the handlebars. If the movement feels "lumpy" then it needs adjustment. 
Riding a bike that has more aggressive geometry than we're used to. You could try borrowing a shopping bike (the kind with an upright riding position and a basket on the front) to see if it's easier to control. If this is the case, then more practice on your own bike should solve it. Meanwhile, as Criggie said, try stopping more quickly so that you spend less time at low speed. 
Being out of practice. If the first two suggestions don't help then the solution is just more practice. 


Take care.