Since my reversion to the Catholic church about a year ago, I have realized there is a tension between those who are more traditional and those who are not so. I have really enjoyed learning all the things about my faith I didn’t know before, and it’s funny because when I reverted, I almost immediately learned about this way of making the sign of the cross (with thumb, index finger, and middle finger pressed together) and began making the sign of the cross that way and continued to do so for some time.
It’s just preference, and her children are unlikely to be all that affected by it, but it seems she is associating it with traditionalist catholic beliefs about ritual and liturgy somehow, and her opposition is actually to those things. Or she may be merely misinformed and thinks it is actually incorrect to do it that way.
Making the sign of the cross with an open hand represents the 5 wounds of Christ (each of your five fingers).