You can certainly have a Mass intention for your deceased mother. While there is no fee for a Mass intention, it is recommended that the person requesting the intention make an offering. Usually the recommended offering is $5 or $10 per Mass (sometimes a little more if music is involved). However this recommended offering in no way, shape, or form can be required for the Mass intention to be said (canons 945 §2, 947).
This may all be a misunderstanding. I would suggest talking to the priest again.