We have a real dandelion problem here where i live, so i get quite a few as well. They deffinately are the reason for your aphids.
Plant some roses if you can, they will help keep them atleast centralised and pestering the roses instead of other things in your garden.
Honestly i wouldnt worry to much about them pestering your trees, they leave mine alone, certain species of tree you will have to watch more than others, but if you keep an eye on them, they are easy to spot quick and stop.