Hello Jacqueline ,
I too had trouble with huge roots having moved home not quite a year ago , my son-in-law used every implement he could including a pick axe ! i too live on the coast ,always have , albeit the north Kent coast ,and in the past i have had to work a lot of compost into the ground to break it up , especially as it is a very clay soil and can set hard , unlike your rocky ground , but once it rains it makes the ground a lot easier to work , it does take quite a time though , as for hedging there are several plants that would suffice depending on how tall and thick you want the hedge to grow you could try some forms of conifer , the 'red robin' is fine if planted fairly close and is evergreen , also Tamarisk , a real sea side favourite ,along with the Hydrangea , and some Oleanders , all of which i have in my garden , also the privets and euonymus !.
The important thing is not to give up , ( pity about the original hedge , hope you got some satisfaction as to why it died ! ) I'm afraid that is all i can suggest and wish you luck .

It might be easier to give up on a lawn and have a paved area instead, (Never thought I would ever say that...) There are several sites on google with lots of information on what will grow right on the coast. Try putting in Seaside Garden Plants.You'll get info on shrubs as well as perennials so it may solve your hedge problem.
Near here right on the coastal path there's a group of Rosa rugosa which flourishes there and has great hips in winter too.