Do not try taking them to small claims court. they will win and you will be out more money. By law you are entitled to have some means to contact the owner. Look at your rental agreement to see if the owner address is there. If not request it from the management company. Or look up the property on the tax assessors page for the owner info. (Myself or another Realtor can help you with that)
You probably won't get back the money you spent but maybe if you work with them they can give you credit on your rent. Also, it may be its not the management company but the owner is balking at doing the repairs. Property managers only keep a small reserve, usually between 300 to 600 for each property. And, as someone else said, if there is no health hazard they can take their sweet time. If pool service is not one of the things you are required to pay then don't. I would be curious as to what is wrong with the pool? I am a property manager myself and sometimes we are caught between owners and tenants. And sometimes its just bad management.
Lockhart & Associates