I would be very hesitant to ship a sewing machine. But my travel machine fits into my carry on and I have flown with it several times. Considering the state of the world right now, I would opt to drive if at all possible, and pack everything into my vehicle.
Also, speak to the relative and find out how much space you will have in their home and what kind of supplies they might already have--such as an iron, ironing board, extension cord(s), table and chair suitable for sewing. You might also do an online tour of the area to see what kind of services and stores will be available to you.