My family says that birthday parties are not major sins.

Answer

If your family does not consider a wrongful act as a 'major' sin, then it means that at least they consider it to be a 'minor' sin. The consequence of both 'minor' and 'major' sins is the Fire of Jahannam. Can your family bear the heat of the Fire of Jahannam?

The division of sin into 'major' and 'minor' is of technical import. As far as practice is concerned, all sins are major. There is no 'minor' sin in terms of practice. The Mashaaikh say that whoever believes a sin to be minor, practically, believes Allah Ta'ala to be 'minor' – Nauthubillaah.

To show love for children, they have the whole year. Why must it be shown in kuffaar customary style? They labour in self-deception, duping themselves with their baseless argument of justification. From whence did they gain the idea that love and affection should coincide with kuffaar customs? Emulation of the kuffaar is haraam. Whoever emulates a kuffaar practice/custom is of them. May Allah Ta'ala guide them.