Oh I totally understand the struggle, a few of us had the same problem and honestly the best solution we found is getting a good stroller rain cover with ventilation holes, so baby stays dry and you can just focus on pushing with both hands without needing to balance an umbrella at the same time. My neighbour actually swears by this too, she got a plastic one that fits snugly over the pram and said it made such a difference on those sudden afternoon downpours we always get here. Some mums in our group also recommend getting a UV-protection umbrella that doubles for rain, so on days the cover isn't enough, at least you're protected without carrying two different things. Just make sure the rain cover has ventilation so it doesn't get stuffy inside for the little one, a few mums had issues with the cheaper ones that trap too much heat!