The OP asked if there is responsibility with the store, and I said no. Is it just one of those things? Again, no. She had a lapse in judgement and supervision with her children.
Please note, I did say that we ALL have lapses at some point, but that it still is technically our fault. I've actually had a trolley tip with DD on the side years ago when she was 4 (she wasn't injured, but it was embarrassing as she fell into an open freezer bin - right into the chips section! ). I don't blame anyone but myself, as it was a similar situation. DD had a habit of climbing on the side, I knew it, and I told her off repeatedly but didn't take it any further. For me, that was a bit of a wake up call, as she could have been injured, especially if it'd fallen to the floor with her under it. I felt the same way about my own behaviour (irresponsible about not being proactive about the problem and not paying enough attention) that I do about the OP.
There are signs about what is considered safe trolley usage. One would think that common sense would suffice, but apparently not.
I'm by no means a perfect parent, but if you knew your child was doing something repeatedly that could potentially cause them injury, and they do it despite you telling them off on a number of occasions, common sense should tell you that further discipline or other methods to solve the problem need to be taken. I do think that as a parent, you have to take responsibility and use some common sense.