The Roman's sacrificed at the eastern gate (like your quote says), not inside the temple, because by then the temple had burned down:
The Jewish historian Josephus -
"7. And now, since Cæsar was no way able to restrain the enthusiastick fury of the soldiers, and the fire proceeded on more and more, he went into the holy place of the temple, with his commanders; and saw it, with what was in it: which he found to be far superior to what the relations of foreigners contained; and not inferior to what we ourselves boasted of, and believed about it. But as the flame had not as yet reached to its inward parts, but was still consuming the rooms that were about the holy house only; and Titus supposing, what the fact was, that the house it self might yet he saved, he came in haste, and endeavoured to persuade the soldiers to quench the fire; and gave order to Liberalius the centurion, and one of those spearmen that were about him, to beat the soldiers that were refractory with their staves; and to restrain them. Yet were their passions too hard for the regards they had for Cæsar, and the dread they had of him who forbad them: as was their hatred of the Jews, and a certain vehement inclination to fight them too hard for them also. Moreover, the hope of plunder induced many to go on; as having this opinion, that all the places within were full of money: and as seeing that all round about it was made of gold. And besides, one of those that went into the place prevented Cæsar, when he ran so hastily out to restrain the soldiers: and threw the fire upon the hinges of the gate, in the dark. Whereby the flame burst out from within the holy house itself immediately: when the commanders retired, and Cæsar with them; and when nobody any longer forbad those that were without to set fire to it. And thus was the holy house burnt down, without Cæsar’s approbation." (The Wars of The Jews, Josephus, Chapter 4.7)
The Daniel 11 events by the "vile person" requires a STANDING TEMPLE in Jerusalem, not one that burned down before the Romans could get control of it. Your theory is only interested in the Romans having done sacrifices anywhere in Jerusalem to try and prove Daniel 11 is history. Thus you're not following what Christ revealed about the future Daniel 11:31 event that is for the end of this world...
Matt 24:15
15 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:)
KJV
That holy place means in the temple, like what Antiochus Epiphanes did in 165 B.C. with sacrifices swine upon the altar and placing an idol abomination in Zeus worship.