Uh... I really don't know what you're driving at but you're going completely off the rails. Death is not the end of existence, it is the separation of the physical body and the soul. Soul animates (enlivens) the physical body which is why all living things (animal and vegetable) are said to have souls proper to their nature.
Meanwhile, there is a danger of straying into heresy in some of the descriptions of the Trinity that have been posted lately. According to Augustine "the Father, and the Son, and the Holy Spirit, as they are indivisible, so work indivisibly. This is also my faith, since it is the Catholic faith."
The Catholic Encyclopedia entry on the Trinity has this note on Augustine: "He insists that every external operation of God is due to the whole Trinity, and cannot be attributed to one Person alone, save by appropriation".
What has actually been expressed by you earlier is "tritheism", I'm not making it up, it's a condemned heresy that denies the unity of the Divine Being but also the unity of the Divine Operations. Saying that one thing is exclusively the work of One Person is tritheism. When God acts, GOD acts.
So God the father died on the cross and impregnated Mary