Question
I have recently had little sucker trees..I suspect an old maple tree probably 40 yrs old had been cut down..several yrs ago before I moved in to my house..I have a forest of tiny trees all over my lawn...I cut them with the lawn mower but they come back thicker and harder.impossible to walk barefooted..I got my ax and started to cut them out and have discovered these big roots about 6-8 inched down all over my yard...I could chop away hours all day and not even begin to get them...help I feel like I am being taken over my all these little suckers...thank you for any advice you may have for me

Answer
Without knowing the genus of trees, I can offer but general advice.  If these are actually suckers and not seedlings, than you probably have in invasive genus of tree, sprouting from roots left in the ground.  The removal of the roots is important.  Plowing or excavation with the right sized implement should remove the problem.
If they are seedlings, you may plow them up and resew the lawn with reasonable success.  Alternately, a 2-4D blend will remove the invasive woody plant and favor the turf, if it meets your quality expectations without renovation.
Be careful with any strategy not to damage the roots of trees you wish to keep on the border of the lawn.  If the area is small and trees are everywhere around it, you may do well to import soil to cover 2-3 inches and resew on top of it.  When the sprouts return, treat them with a 2-4D blend, as recommended by our local ag agent.  There are some products on the market with truly amazing results.
Best of luck.