here is what i know
Al Kanz (look up the yellow pages for their number, sorry) trading helped me arrange a transit saudi visa the last time i drove to dubai.
if you are on the same profession here you should be able to get a visa to saudi and bahrain-on arrival.
regarding your mother, since she is on a visit/tourist visa she will not have the same benifits as you. her visa will need to arranged by somebody in saudi and bahrain respectively IF it is possible.
as far as i know.. its not possible for visitors to get a transit visa to saudi or bahrain if they dont qualify.
hope this helps.
good luck... i too may be heading to bahrian for EID holidays.