Single pivot brakes don't have a sufficient leverage. For a given amount of movement of the arms (and pads) towards the rims, the amount of movement at the levers is low. The less the movement, the greater the force required. This is fine for many of us guys with large, strong hands. Road racers preferred these brakes because they gave good feel for minute modulation. But they're not well suited for smaller hands, and they're very badly suited for bikes loaded with weight. I made the mistake of taking an extended tour with brakes like that when I was young. I compensated, but I'm lucky to have the hands I have. I wouldn't so it again.

Dual pivots are a different design that apply great force to the rims with little pressure required at the lever.

if you're comfortable using the levers from the hoods, then don't bother with the interrupter levers. Change the calipers first. This is easier than fixing a flat.

Mixtes have almost completely disappeared from the US market. I don't completely know why, but I suppose one factor is that diamond frames, being superior and lighter, now come with sloping top tubes, which reduces the need for a separate design for women. Another is that not many women want to ride wearing dresses or skirts. The sloping top tube is OK for shopping unless the rider is going to carry a heck of a lot of cargo. In that case, they now make city bikes with no top tube and no substitute. They have gigantic down tubes to keep the frame relatively stiff, but they're pretty heavy. That's OK for short trips, but it's not the type of bike you would ride for fun on weekends.

Another development is that modern bikes often have shorter reach from seat to handlebars, especially in the women-specific designs. Check that yours isn't too long. If it is, you may end up preferring a different type of handlebar.