I am assuming that you are living in atleast a three bedroom apartment ( since there's a grandma and u still have a spare room for rental).  So, ok, basically you want a roommate who will use only one bedroom and pay half of the rent for three bedroom apartment?  
 And in addition, that person has to provide some extra service for driving ur kid to school or whatever to you?  For what?  to save some bucks on utilities and internet?  Since there are already four ppl in your family, it's obvious that most of the utilities gonna be consumed by your family.  So here, the actual deal your roommate is getting is to save few bucks on the internet.  But, who is going to pay for gas on your kid's school trip?  I don't think you will compensate for that. Even if you want to, it'll not be practical to calculate it. I don't see any monetary gain your roommate can have. However, s/he will gain a lot of headaches for dealing with four ppl and will lose his/her all privacy.  So, actually in this deal, YOU are the one who'll enjoy all the benefits and your roommate will pay more than necessary to become your driver for the kid.  I must say you are a very good business man !!