1. I am about to receive a gift for my two sons (2) and 5 yrs old, $50,000 each but the money is in a foreign
Country. How should my relative transfer the funds, in increments less than $10,000?

2. Will they need to file and income tax return?

Any other suggestions will be greatly appreciated.

1. About Gift Tax.
In U.S. the receiver of gift does not pay any gift tax. Only the donor of the gift is liable of gift tax. If the donor is a foreign person (that is the person is not a U.S. citizen or resident), the donor is not covered by U.S. taxes that is donor does not pay any U.S. tax. Your U.S. Tax Return: The U.S. Gift Tax

2. Getting Money to U.S.
You can get any amount from a foreign country through your bank. The $10,000 is limit from bringing currency notes (or cash in any form) to U.S. By wire transfer to your bank account you can get even 1 million dollars.

3. However, since it is coming from a foreign country, the IRS wants to make sure that it is a actually a gift. So the receiver of the gift from foreign sources must file File 3520 Annual Return To Report Transactions With Foreign Trusts and Receipt of Certain Foreign Gifts if the amount if the total gifts received is more than a certain amount. Check if you will be required to file Form 3520 or not.