I am English and have lived and worked on the Westside for 33 years, including the last 10 years in Santa Monica (my favourite), which has a great school district, parks, farmers' markets, etc. I would love to help you and your family find a great house to rent in Santa Monica.
As you have probably not yet established a credit history in the U.S. you will need to provide proof of funds and ability to pay (e.g. copy of a statement from a local bank account, you can black out the account number for privacy, letter from employer) and work visa. You will need to pay a deposit of a minimum of 2 months' rent and sign a rental contract, usually for at least one year, after which it may be on a month-to-month basis.
Please call or email me for more information. I can email you current listings to match your criteria, to give you an idea of what is available.
Good luck and I hope to hear from you soon!
Keller Williams Santa Monica
cell 310 739-7937