Because of these factors and others that should be considered, it is recommended you work with a strong Qualified Intermediary and advisors to help make the best decision for you and your family.

The 1031 has to begin prior to closing of the sale with an agreement with a qualified intermediary.

You are right on the money regarding the requirement to exchange rental/investment property for other rental/investment property, that it must go through a mediator (Qualified Intermediary), and that the taxpayer/investor can not touch or have access to the net proceeds from the sale of the rental property. 

The most important key is that you must use a qualified intermediary to document the exchange and they must be in place prior to closing your sale.  

I know here in the US, you can avoid those taxes if the property was your primary residence for at least 2 years, but I'm not sure what the US law requires when you sell a property from a foreign country and try to bring the money to the states.If we do have to pay taxes on it, has anyone worked with a 1031 exchange intermediary that they might recommend to help us with this process?  

You may even put earnest money of your own down now and have it returned at the closing of your purchase so only the 1031 proceeds go forward.What will impact your exchange though is if you do not have a qualified intermediary in place prior to the close of the sale.  

Either he acts as an intermediary for both you and the seller (both you and seller must agree to this), or he is an agent of the seller and acts only in the interest of the seller with you representing yourself in the transaction.Since in almost all cases the seller pays both sides of the real estate commission anyway, you should contact a different real estate broker and sign a buyer's representation agreement.  

This will increase deal flow because stronger operators that have avoided the marketplaces will now have the tools to raise money all on their own without the need for an intermediary.  

If an intermediary is not in place and the 1031 is not reflected on the settlement statement  then your opportunity to do an exchange is forfeit.  

They are serviced by a person called a qualified intermediary.