Please help me get sunlight and mess free garden

At my backyard there is a huge tree, which is actually grown on the back garden of 114 property which is as per my knowledge is council property ,is covering all my garden's and house light and my neighbour's too .It shed leaves,fruits and seeds throughout the years which is very difficult for both of us(property 118 and 116) to take care off. Me and my husband love gardening and want to grow some herbs and vegitables but unable to fulfill our dream of doing it due to shade of this huge tree also its seeds grow very fast and aettle deep rootsin a little amount of time and very difficult to pull out even there are half a dozen more simmilar young trees grown at the back of our yard which is in some property behind ours at popple street . Please help us keeping our garden tidy and get sunlight which is blocked due to these set of trees . We found it very difficult with our little girl who is just 16 months now ,she pick leaves and other shedding stuff from tree and try to eat ,I am struggling very hard with my hand issues as I have Carple tunnel syndrom (my hands hurt all the time ,and it is difficult to clean back yard three or four time every day and keep it clean ) . Please ,please help us by removing these set of trees or atleast cut huge branches of them to reduce the problems .