I would take my child to the mosque often when she was a baby as at that age all she would do is sleep, so it was easier. But now she is a toddler it is a little harder as she does what toddlers do best now. I only take my daughter now when offering short salaats.
I always see endless toddlers running around in the Mosque. This is natural for young children to do and women have become accustomed to praying with children running around and talking. I personally don't mind if kids make noises or talk as I have a lot of patience where these things don't bother me. But some do get bothered by this and cannot concentrate on their prayers.
I believe woman and children should be encouraged to go to the Mosque but don't blame your child for not sitting still or talking as I think it is really hard for a toddler to do such things while their parent read 18 rakats of salat or something! This is unfair on the child and unfair to worshippers around who can't concentrate. So if this is the case, then prehaps it is best to pray at home until your child is older. This is unfortunate but I think many women deal with this.
Maybe you could take a sister with you and you both could rotate while one reads Salaat and another is outside playing with the child. I have seen some women do this. :)