Is it ok to move my computer (desktop comp) from my mums to my dads every week? its like a 3 minute drive
Nothing can be damaged in doing so, other than perhaps the hard drive if you are using a mechanical one and manage to shake it about too much. So, i'd say it's fine.
As long as you can carry it steadily its more than OK. I (personally) wouldn't be bringing more than a mid tower around town, but that depends on your strength and confidence. Also, if you have a large heatsink and long GPU make sure they're secured well (but not too tight).
I personally use my desktop to DJ weddings up to 9 times a week. It is actually more durable and secure than a laptop in that it's weight keeps you more mindful of it and makes you more concentrated on how you place it. The only time I use my laptop anymore is to DJ parties and bars.
Just don't drop it or give it shock. The only thing that you should have to worry about are hard drives creating bad sectors.