Well, I do caution you not to demonize egg yolks too much, they are also considered the healthiest part of the egg, not just the most caloric, and still very low in calories for the nutritional punch they pack
Consider this, when you feel like stuffing your face with icecream because you are upset - food is NOT a bandaid, or Prozac, nor is it a friend. These things help emotional and physical hurts, food helps hunger. Letting food help more than that is ASKING for a regain. Dealing with emotional eating is one of the hardest struggles many of us (me included!) often face, but it CAN be dealt with if you put food in its' proper place as nutrition to fuel you, not as balm to your soul.
If your plan has you not eating egg yolks, don't eat them! Tell your mom that this is your diet and if she cannot say something constructive, kind, or supportive, you would prefer she not say anything at all because it is hurtful to you. And then tell YOURSELF that the best revenge for those hurt feelings is a healthy, on plan day WITHOUT proving her right. Because it's true!
You can do this, but you need to get a solid handle on your emotions first. Saying no to food when you are not hungry is going to be your biggest leap forward, just as important as choosing a fruit parfait in place of that icecream when you ARE hungry!