The brothers and their father were going for a day out
Brothers Arron and Ben Peak, aged 10 and eight, were killed in a crash on the M6 in Staffordshire on Saturday.
Their father, Philip Peak, is seriously ill in hospital with a broken neck and back.
Plymouth Argyle goalkeeper Luke McCormick has been charged with two counts of causing death by dangerous driving.
Amanda Peak attended a news conference on Sunday in which a statement prepared by her and her husband was read out.
Both Phil and I are devastated at the sudden and tragic death of our two beautiful boys, Arron and Ben.
No parent should ever have to go through the nightmare that we have gone through.
Arron was my eldest son, loved life and especially football at which he excelled.
Ben was a happy loving son and brother and nothing will ever compensate us for the loss we are feeling.
This is also true for all our relatives including grandparents and uncles and aunts.
Both the boys were excited to be going with their dad and friends to Silverstone for a fun day out.
Phil my husband is not only having to come to terms with the loss of his sons but he also has to cope with the serious injuries he has sustained and remains in hospital.
I would appeal to members of the public who may have witnessed the incident that took place on the M6 southbound carriageway near to Keele services at around 0545 hours on the morning of Saturday the 7th of June to come forward and help the police with their inquires.
My family and I would appreciate if we could be left alone to grieve and try to come to terms with this life changing event that has devastated our lives.