This explains this even better. Here Carrier demonstrates with examples and links to several papers on the subject on how Mark uses Paul's Epistles in crafting his story.
Mark's Use of Paul's Epistles • Richard Carrier
He also demonstrates a chiastic structure that Mark uses using Paul's writings that would be incredible unlikely that he wrote this independent.
One example is how Mark created the last supper from a statement from Paul. Paul claimed during a vision Jesus said:
"For I received from the Lord what I also handed over to you, that the Lord Jesus, during the night he was handed over, took bread, and having given thanks, he broke it and said, “This is my body, which is for you; do this in the remembrance of me.” Likewise also the cup after supper, saying, “This cup is the new covenant in my blood; do this, as often as you might drink it in remembrance of me.” For as often as you might eat this bread and drink the cup, you proclaim the Lord’s death until he comes"
Mark changes this into an actual event with people:
"
While they were eating, having taken bread, and
having blessed it, he broke it, and
gave it to them, saying, “
Take; this is my body.” Then, having taken a cup, and having given thanks, he
gave it to them, and
they all drank from it. And he said
to them, “This is my blood of the covenant, which is
poured out for many. Truly
I tell you, that
never again shall I drink from the fruit of the vine, until that day when I drink it anew in the kingdom of God.” And
having sung a hymn,
they went out to the Mount of Olives."
Carrier points out:
"Notice what’s changed. Paul is describing Jesus miming some actions and explaining their importance. His audience is future Christians. Mark has transformed this into a narrative story by adding people being present and having Jesus interact with them: now “
they were eating” (Paul does not mention
anyone actually eating) and Jesus gave the bread “to
them” (does not occur in Paul) and instructs them to “take” it (no such instruction in Paul); and Jesus gave the cup “to
them” (does not occur in Paul) and “
they all drink it” (no such event in Paul); and Jesus describes the meaning of the cup “to
them” (no such audience in Paul).
Then Jesus says he will not drink “again” until the kingdom comes, a statement that fits a narrative event, implying Jesus drank, and here drank, and often drank, and will pause drinking until the end times. Likewise Jesus “blesses” the bread (which also doesn’t happen in Paul), implying the actual literal bread he has in his hand is thereby rendered special to the ones about to eat it; whereas in Paul that makes no sense, because no one is there to eat it, Jesus is just depicting and explaining a ritual
others will perform in his honor, not that he is performing for them. So it is notable that all of these things are absent from Paul. There is no narrative context of this being the last of many cups Jesus has drunk and of Jesus pausing drinking or of his blessing the bread and giving it to people present. In Paul, the whole scene is an instruction to future followers, not a description of a meal Jesus once had.
This is how Mark reifies a revelation in Paul, relating Jesus’s celestial instructions for performing a sacrament and its meaning, into a narrative historical event. Mark has even taken Paul’s language, about Jesus being “handed over,” which in Paul means by God (
Romans 8:32, exact same word) and even by himself (
Galatians 2:20, exact same word), not by Judas, and converted it into a whole new narrative of a betrayal by “the Jews” (the meaning of Judas, i.e. Judah, i.e. Judea). Paul has no knowledge of a betrayal. Indeed in Paul, all of “the twelve” get to see Jesus right after his death and are recognized as apostles (
1 Corinthians 15:5.
He also points out Clement 1 uses this story before Mark but doesn't know about Judas because Mark hadn't invented it yet.
So this and many other examples give evidence that Mark used Paul as a source as well, which explains the brother thing.