How can I run a line under a cement sidewalk
Unless you want to get into concrete repair here and need an excuse, dig a 5-6 foot long pit on one side of the sidewalk, and a 1 foot long pit on the other side. Drop pipe into the 5-6 foot long pit, hammer in. Run a hose up it and flush the dirt out (probably not continuously - it's easy to overdo) and drive some more. When it pops out on the far side you are done. Won't work if you hit a big rock. Cut the turf off neatly so you can patch the hole in the lawn when you are done, or just do it in the flowerbed and put the plants and mulch back.