Our Prophet(Peace be upon Him) never disallowed children from coming to the mosques. Rather he encouraged them even if it meant that they may play around and not actually pray. In fact their is a hadith where his grandson climbed on his back whilst he(Muhammad) was in prayer, and another where when babies used to cry he would shorten the prayer so as to not burden the mother. Such was the practice of our Prophet.
People today though are far more temperamental and less tolerant than the Prophet and His companions. As a result many mosques tend to even have heated rows among the people with regards to kids and them disrupting the prayers etc. Mind you I have witnessed these myself and trust me they are not pretty! Hence nowadays it's much better for the parents of kids to avoid bringing them to the mosque due to the kind of troubles it can cause.
Personally I avoided taking my daughter to mosques until she started praying a year back. Better safe than sorry!