I am no expert but I would say that calling her and validating her sadness and thanking her for the gift would be a good idea. Then if you feel you should get off the phone ASAP do that. But I guess from a purely woman's standpoint, I would not feel good about putting myself out there with a small gift and not at least getting an acknowledgement.
Everything happens for a reason, maybe Dad needs to find that it isn't better out there, he needs to realize how good he had it here. Maybe he will find God and that is the most important thing when he finds Him he will know he is supposed to come home.