Don't do anything until you have changed the pressure gauge. They are cheap, maybe 5 bucks. If you then always show good pressure at the well pit, even while the water trickles in the house, then maybe the tree root thing is possible. If the pressure on that gauge is low when you experience the "trickle", then you have other problems. Maybe you just need to replace the filter cartridge more often. Or the large amount of sediment could have damaged your pump or stopped up the well.