Moving to ras al khaimah with family

RAK is a relatively older, upcoming Emirate.  It has lots of old structures and streets, same time a good amount of new developments like fantastic golf course, malls etc.  It is somewhat quieter than the hustling bustling of Dubai.  Rents are cheaper in RAK, in any case you are covered.  Food expense is not much, initially you can do with minimal furnishing (if not provided by company).  You can manage within 2500 dirhams, if medical insurance is covered.  Make sure of the medical part.  If your child were going to school, that could be a bit expensive, can cost you even AED 2000 per month, depends on the school.  Right now you do not have that issue.
RAK is about 100 Km (plus a few more depending on where you stay) on the highway.  There are public bus transport as well as taxi services available, till such time you are able to obtain a driving license and a car.
Though RAK is slighly more conservative than Dubai, there are no hard dress codes in the UAE.  This is not Saudi Arabia!  So be comfortable in what you wear, so long as you do not offend people with too much revealing dress.
RAK is quite safe for everybody.  They respect families everywhere in the UAE.  You can have a good fun with your kid here.