M.S.
If she is going that much so that it clogs the toilet then she needs help. You should talk to your pediatrician. The messy panties is because the loose stuff is coming out around the big blockage. I think this might be what is lubing the big one so that it can come out. Its always been my understanding that a person should go once a day about the same time everyday, and if they don't then there is something wrong. Going 3x a week is too little!
My pedi said that once it hurts to go they will hold it in. He said to give my 2.5 year old 2 doses of miralax every day (full adult doses) until she has 2 or 3 bowel movements every day for at least 2 weeks. This will get her used to going and it not hurting. There will probably be a few accidents, but it will be better for her in the long run.
I would call your doc and talk to him, or take her in, but this is NOT normal and its not OK. You don't want her to end up with IBS or some other issues later in life if you can stop it now. Good luck mama!