it is not the smaller tirangle that causes step through frames to be weaker
but the lack of support on the back side of the seat tube where the lowered top tube joins
a normal non step through frame has the top tube and the seat stays meet the seat tube at approximately the same place
so the seat stays and top tube sort of cancel each other out

there is a third type of frame called a mixte which are not commonly made anymore
these frames have the same front half of a stanard step through frame
but the rear half has an extra set of seat stays in the middle between the seat stays and chain stays
meeting the seat tube at the same point as the top tube

mixte frames were much more common in the 70s and 80s
but went out of style when many bikes started being made with sloping top tubes and cmopact rear triangles
a few smaller companies are still selling them but not in huge numbers
http://www.somafab.com/archives/product/buena-vista

anyways
yes step through frames are not as strong as standard frames
but they are still more than strong enough to handle regular street riding
even with large bumps and bunnyhops to clear obstacles

edit

just saw that you have a mixte frame
in that case
ride it like you stole it
it is as strong as the same bike in the non step through version