This is a problem we face alot with our 3 year old. The doctors have him on a daily dose of miralax. It's a softener in powder form that we put in his drink before naptime. It has done wonders and is fine for him to take daily. For now, since you are dealing with the need to go ASAP, drop milk products. It makes a huge difference. My son still has milk but if he gets backed up, we stop it until he goes. Or, we water down his milk.
Yogurt is supposed to help with digestion. You could try that for eating. Stear clear of bananas, rice, apple juice. If she will eat an apple (needs the peel for fiber), try that.
We have such a hard time with this so I wish you luck!