mr alan fisher

I have been a regular gardener for aprox 40 years,mainly vegi,but in the last 5-6 years I have turned to flowers,i am ok growing in the green house unheated but as soon as I put them outside some die so now I always grow extra incase. I think it could be the neighbers 3 large conifer trees because each year I dig up lots of roots,.can anyone give advise on how to get rid of these shoots coming into my garden,