I also find myself feeling angry when I look at my wife's picture. I can't believe I would be mad at her for getting sick. Your wife's death has precipitated not only the loss of your life's partner, but a dramatic alteration in your lifestyle. Your path to recovery has included experiences you had not bargained for. Becoming a single father to two very young children and managing your own and your children's grief has been an enormous challenge.
Anger is often a stage that follows sadness in the grieving process.
It is not surprising that these feelings would arise as you are beginning to date. Acknowledge, but do not judge your feelings. It is natural to experience feelings of abandonment which can trigger both anger and sadness when a spouse dies. Mourning and sadness allows us to gradually let go, as to some extent we experience the person with us in some way. When you begin to date, you are beginning to move on towards the possibility of a new family constellation, a new possibility for partnership.