Is my sitting and eating with my Christian family while they bless the food by mentioning the name of Jesus or "Our Father in Heaven" considered shirk (polytheism) or injustice to myself, even though I do not believe in what they say? And what should I do if my refusal to sit causes their displeasure?

All praise is due to Allah, who guided and blessed you with Islam. We advise you to treat your family with kindness and gentleness in your call to them. Indeed, the request of Jesus (peace be upon him) to bless food is major shirk because it is supplicating to other than Allah Almighty. Therefore, it is not permissible to participate in it or to remain silent about it. If you are unable to denounce it verbally, then denounce it in your heart while leaving the place, for Allah Almighty says: (And He has already sent down to you in the Book that when you hear the verses of Allah being denied and ridiculed, then do not sit with them until they enter into another conversation. Indeed, you would then be like them. Indeed Allah will gather the hypocrites and disbelievers in Hell all together) An-Nisa/140. So, if they begin to supplicate, denounce them or rise from among them. It is preferable to delay slightly until they begin eating. If your family accepts your invitation (to Islam), explain to them that Islam places great importance on enjoining good and forbidding evil, and it does not condone supplicating to other than Allah, nor does it condone affirming reprehensible speech.