If you seriously think that by giving your kids free access to the internet, you are showing them that you trust them, and all will be well, you are sticking your head into the sand. Do you know what is going on out there? Kids from good, frum families are going off the derech because they had access to unfiltered internet. Don’t tell me that they would have found a way to go off either way. By giving them internet in the comfort of their own home, you are inviting them to stray. It is true, they may go to friends houses or the library if there is no internet in your home, but at least it is not so accessible to them!
Kids crave boundaries and stability. They test the rules to see what they could get away with, but if there are no rules, they feel lost. Having filtered internet or no internet at all is not telling your kids that you don’t trust them. It is showing them that you are a family that listens to the words of the gedolim, because they know better than us. If you think that by going against the psak of the gedolim, you are giving your children a feeling of trust, you are sorely mistaken and I feel very sorry for you.