Daniel,
As Rod poited out it is certainly possible to motorize your dobson and it is not hard to do :-)
Have a look at
Mel Bartels website for mechanical details.
Computer is not such a big/bulky problem, I am still using an old Fujitsu Stylistic 1000 for that purpose (I bought it from ebay for couple of $$.. I am using it because it still works and because Bartels software supports encoders, which are great for manual / visual - once aligned, user just needs to stop tracking, move to other object and restart tracking, software will calculate necessary parameters from encoders readings), but you can try with other systems as well, lile
OnStep or
AstroEQ, both use cheap parts usually used for 3D printers and small CNC machines.
Soundstepper is also good (unfortunately, neither of those above support encoders - which is what is needed to mitigate issues Billyboy78 is mentioning).
I can help you with electronics, I even have couple of spare PCB's (suitable for Bartels-OnStep-SS in my drawers.