Social Security Benefits

I am disabled an receive SSDI benefits. Both of my Children are young an also receive Social Security Benefits because I am disabled. Both of my children get a FORM SSA 1099 at the end of the year. MY younger son lives with me full time so he is our dependent. My older son lives with his mom 40/60 an I have his benefits assigned to her directly as she claims him on her taxes. My Question, Do I open a separate filling for my younger son an do his taxes based off the SSA-1099 Fed an state or am I suppose to claim his benefits under my taxes instead? I am also assuming my older son whos benefits are assigned directly to his mom is responsible for claiming his taxes as she would have gotten his SSA-1099 statement an claims him as a dependent but told her I would give her a heads up as I am not exactly sure how that is suppose to be claimed.