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Sorry to hear that. I hope she get's well quickly.
As an aside, we have (the occasional care of) two dogs and I can deal with both simultaneously no matter what. The Mrs normally takes them out in the morning but one_at_a time because she can't.
It's not the issue that they are big dogs that always pull and she a little / weak woman, they are medium dogs that if they see a cat could catch her out and at nearly 70, isn't as fit and surefooted as she was (even with her new knees). ;-)
Before the big terrier became more socialised (rescue dog), I have had him suspended in the air on his harness with just one arm.
That doesn't mean either of us could maintain our balance on slippery surfaces, with or without the dogs. ;-)
Cheers, T i m
p.s. When we started dog-walking (in all weathers and across multiple terrains) we researched different shoes / boots that might keep our feet dry in the wet and offer reasonable grip. Some soles were extremely slippery, even though they looked like they might offer reasonable grip.