I go to a baptist church and we only do dedications. Baptisms are done once the person is old enough to make a concious choice for Christ. I am not sure about other denominations to be honest, but my sister (who isn't a believer) got her daughter baptised / christened in an Anglican church.

There was a baby dedication on the fathers day service a few sundays ago. It was lovely, the parents were commiting themselves to raising up their child in the ways of the Lord, the rest of the family promised to help and support the parents to do that, and the church also promised to support the whole family. Overall I was impressed, it was lovely.

You could explain it to the other families members like this: We are doing this in response to these scriptures

Proverbs 22:6
Train a child in the way he should go, and when he is old he will not turn from it.

and

Ephesians 6:4
Fathers, do not exasperate your children; instead, bring them up in the training and instruction of the Lord.

and later when they are older they may choose to be baptised. But explain that these are two seperate events.

I hope this helps! We cannot please all people at all times, so just go with your conviction.