Repairing a threadbare lawn
I need some advice about how to go about repairing my lawn. The part of the lawn that needs some serious TLC has never been lovely as the clay soil is quite compacted and it is under a large cherry tree so has always been dry. I aerate and dress it every year but it was fairly awful. However it has been completely trashed by the two lovely rescue dogs we adopted last year who just love to run up and down the garden and particularly like to play fight under the cherry tree - photo attached with the dogs on their naughty steps!
I'm pondering two ways forward (the option of getting rid of the dogs is not an option at all!). One is to plant robust dry shade loving plants under the tree and mulch around them and then try to salvage the rest of the lawn. Alternatively, and most likely, I'm planning on replacing the lawn but have no idea how to break up the soil. My husband says he'll attack it with a pick axe but that would be backbreaking. So any suggestions for what tool I should hire to break it up? My plan is to replace the top few inches with new soil and mix in something to help with the structure - suggestions? and to then lay turf (with a dog proof fence around it for at least 3 weeks!).
Any thoughts you might have would be much appreciated.