I would say that region has had its share of dictators that might resemble Abraham and its conquests for the holy land. How many have claimed rights to those lands these past thousands of years. Land promised to Abraham and still not given to him very easily, struggling for these lands even in the bible with gods direct help.
Quran does not mention of such Abraham who was promised any real estate or lands and who hankered after occupying lands as you have mentioned above perhaps from Bible.
Quran mention
Ibrahim who was a righteous person and had a different character. There is one chapter in Quran named after Ibrahim. I would like to quote from it here:
The Holy Quran : Chapter 14: Ibrahim
[14:1] In the name of Allah, the Gracious, the Merciful.
[14:2] Alif Lam Ra. This is a Book which We have revealed to thee that thou mayest bring mankind out of every kind of darkness into light, by the command of their Lord, to the path of the Mighty, the Praiseworthy
[14:3] Allah, to Whom belongs whatsoever is in the heavens and whatsoever is in the earth. And woe to the disbelievers for a terrible punishment:
[14:4] Those who prefer the present life to the Hereafter, and hinder men from the way of Allah and seek to make it crooked. It is these who have gone far off in error.
[14:5] And We have not sent any Messenger except with the language of his people in order that he might make things clear to them. Then Allah lets go astray whom He wills, and guides whom He wills. And He is the Mighty, the Wise.
[14:6] And We did send Moses with Our Signs, saying, Bring forth thy people from every kind of darkness into light, and remind them of the days of Allah. Surely, therein are Signs for every patient and thankful person.
[14:7] And call to mind when Moses said to his people, Remember Allahs favour upon you when He delivered you from Pharaohs people who afflicted you with grievous torment, slaying your sons and sparing your women; and in that there was a great trial for you from your Lord.
[14:8] And remember also the time when your Lord declared, If you are grateful, I will, surely, bestow more favours on you; but if you are ungrateful, then know that My punishment is severe indeed.
[14:9] And Moses said, If you disbelieve, you and those who are in the earth all together,you can do no harm to God; verily, Allah is Self- Sufficient, Praiseworthy.
[14:10] Have not the tidings come to you of those before you, the people of Noah, and the tribes of Ad and Thamud, and those after them? None knows them now save Allah. Their Messengers came to them with clear Signs, but they turned their hands to their mouths, and said, We disbelieve in that with which you have been sent and surely, we are in disquieting doubt concerning that to which you call us.
The Holy Quran Arabic text with Translation in English text and Search Engine - Al Islam Online
Regards