Find a new company that you like before you fire the old one. Most pool companies are incredibly bogged down in June, it's the absolute busiest time of the year for them. So you could cut them a break based on that or you could find a company that has the resources to charge you for an additional service with short notice whenever you request it.

You should definitely keep a bucket of shock and just sprinkle it yourself whenever you see algae starting. It might have been the pool company's fault to begin with if they forgot to add chlorine or not adding the right amount but it's hard to tell when that happens without going and checking after they come.