I have numerous composters in my small garden, a greencone which takes all foods, even animal droppings and bones,a wormery, and 2 compost bins, and a metal cage type composter,which is now used for growing rhubarb with great success, I find if the compost is not breaking down well in a bin I put it into another bin and move the empty bin to another corner of the garden and start again.
i have 4 cats and no rats at all. I found that laying large cardboard boxes on top of weeds for a few weeks clears the weeds, then i compost the cardboard. i have a small garden but lots of containers of flowers which grow very well using the compost.