You have a Yagi feeding an LTE modem in your shed via coax? (BTW, your modem probably has two antenna ports, you should use two antennas with their polarization planes at a right angle to get a much higher data rate)
Have you tried placing the modem right next to the antenna with a short cable, and than route a LAN cable inside your shed? If you're currently connecting via USB, long USB cables tend to be susceptible to interference, especially if they aren't of the best quality, and you shouldn't go longer than ~5 meters with USB 2.0 without an active repeater.