According to the doctrine of Trinity, was Jesus always co-equal to the Father? So I'm trying to understand the Trinity.

I always thought of it like this: Jesus was 100% divine when he was with the Father. In other words, he was fully co-equal to the Father. Then, when he became a human being (on earth), he wasn't 100% divine, so he was not co-equal to the Father. In other words, he was part divine, part human (inferior to the father). And when he rose into the heavens (after the crucifixion and resurrection and everything), he became fully 100% divine again. So basically he's co-equal to the Father once again.

But that's how I always understood it. Does the Trinity support this view? According to the doctrine of Trinity, was Jesus always co-equal to the Father? Even during his lifetime on earth?
The Chalcedonian Definition (AD 451) was a key christological statement of the early church, and is respected throughout trinitarianism.  The first portion of the part relevant to this question emphasizes that Jesus is "truly God and truly man":


  Following, then, the holy Fathers, we all unanimously teach that our Lord Jesus Christ is to us One and the same Son, the Self-same Perfect in Godhead, the Self-same Perfect in Manhood; truly God and truly Man.


But perhaps his divinity was reduced?  The creed continues:


  [Jesus is] acknowledged in Two Natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved and (both) concurring into One Person and One Hypostasis; not as though He were parted or divided into Two Persons, but One and the Self-same Son and Only-begotten God, Word, Lord, Jesus Christ.


So no, your understanding is decidedly not trinitarian – Jesus was simultaneously 100% God and 100% man while on earth; his divinity was not compromised.