we have a 2 year old who does not like to be quiet and our neighbor is calling the cops constantly about us being noisey, and we aren't that loud. she calls if we walk to loud, or he runs around during the day.
That can be a problem, and I have been on the other side of that situation.
The police will not likely cite you for noise when it is within your home, and by your child in a normal sort of situation. They will bring with them a db sound meter and measure the noise level. If it gets above (whatever their policies trigger point is) then you may be warned.
If that happens buy a couple of throw rugs and it may help deaden the sound. Anything will help.
If she continues to complain to the police, and they continue not citing you, then ask them how to stop the harassment by process. If he would answer, then call the duty officer at the station and ask him.
Also be aware that after a number of calls the police may start charging her a fee to respond.
Lastly, you can bring suit for her harassing you about normal daily living in your apartment. You have the right to quiet enjoyment of your living space, and she really needs to leave you alone. For that you may likely need an attorney.
General Practice Lawyer
You are in a difficult situation in that the police are likely to believe the party that calls first in a dispute. However, if the neighbor calls repeatedly, and more often than not the police find nothing happening when they arrive, they will begin to see the pattern. You should document every call made as well as police visit and record what you were doing at the time. You should explain the situation to the police and ask them what, if anything, that they have witnessed upon arrival. If the neighbor continues to harass you and file complaints without good cause the police can give the neighbor a citation. If the problem persists, you could pursue a restraining order against the neighbor, but such orders are not easy to get, so it is important to have good documentation.
The judge will not uphold a citation to a two year old for being loud. It is a natural part of life for babies to cry and toddlers to make noise. Normal noises by children do not violate noise ordinances and could hardly be declared a disturbance or a nuisance by the Court. I cannot imagine the police issuing a citation because a two year old was "noisy," unless that officer never has had, or has been around, children.
You have a constitutional right to enjoy your home and live in peace, and so does your two year old. The limits placed on that enjoyment prevent you from unreasonably disturbing your neighbor through unnatural loud noises, such as loud music, fighting, etc., but no court would, or could, order you to put a muzzle on your child or tell you that you must keep them locked in the house and that they cannot play.
If you continue to have problems you may want to consider going on the offensive against your neighbors. I recommend in that case that you consult with a local attorney who may write the neighbors a stern warning letter or advise you of further pertinent action.