Concern about the pressure on your joints is valid. There is no shame in walking as opposed to running. Listen to your body, test your limits, but don't shame yourself for getting tired! Recovery is just as important, IF NOT MORE important, than the exercise. You can't continue each day if you get injured, so go easy on yourself. Push later, but only because you feel empowered to do so - avoid doing it out of guilt, jealousy, or spite.
Your body is your greatest asset, take care of it and it will take care of you. No need to "punish" it every day.
Long term results will come from feeling good about what you are doing, so please try to find additional motivation outside of the disgust you've begun to feel. This will prove to be a much stronger push for you on days when you don't feel like going. Also, walking with the kiddos and family can prove to be a great way to add more exercise each day without the added strain on your body and schedule.