"I love my family."
Some more examples then:
我爱我的 家人 √√/家庭 √√ （I love my family)
他是我的 家人 √√/家庭 XX (He is my family)
我有 家人 XX/家庭 √√ 问题 (I have a family issue)
圣诞节我送礼物给 家人 √√/家庭 XX. (I give presents to my family at Christmas.)
火灾后我送礼物给受影响的 家人 XX/家庭 √√ (I give presents to affected families after the fire.)
Someone must have taught it as a rule but imho that is not accurate. Personally I would always include 的 in this sentence, though not to the extent that it is indispensable. I also cannot think of any case that not omitting 的 would make a sentence effectively become wrong. At most it would just appear a bit clumsy.