Yes, Jerusalem is the capital of the State of Israel, and has been for over a half a century. This is where Israel's government sits, and does the business of running the country.
The controversy is based on historic opposition to the existence of the State of Israel at all. The 1948 armistice line, called the Green Line from old military maps, marked the division between Jordan and Israel until 1967. In the Six Day war that year, Israel conquered everything from Tel Aviv to the Jordan River in that region. The Oslo Accords returned local governance of non security issues in certain Palestinian areas, including areas to the East of Jerusalem, where Palestinian majorities are pervasive. The final resolution of Jerusalem and its status as capital of Israel and or a Palestinian State was left for last level negotiations. Since then, Israel needed to build a separation barrier on the eastern side of the city for security purposes, and the peace process has broken down. Yet the continual governance of the united city of Jerusalem has continued unabated, and well.
Moving the embassy was delayed for many administrations to avoid "picking sides" in the final status of the City. But that is ridiculous. Should the U.S. put an embassy in an area whose "final status" is in Israel, then it is the embassy in Israel. Should that embassy wind up in a State of Palestine, then it will be the embassy in Palestine. Should it be determined (never) that Jerusalem becomes the United Nations original pipe dream of an International City, then - mazal tov - you have a consulate for the United Nations there. Putting a U.S. embassy building down in Jerusalem changes nothing, except it refuses to cater to the delusion that Israel is not real and permanent. Good negotiations begin with facts, truth and clarity. Opening the embassy does that.
Now, what IS interesting is the piece of land chosen by the U.S. While it has not been covered by the media, the embassy straddles the Green Line. The west side is on the Israeli side of the green line and the east side is on the old Jordanian side of the green line. Theoretically the building can accept people from either side, without controversy. Cynics however will say that it declares Israeli sovereignty by ignoring that it is building "across the green line," in part on "occupied territory."
Personally, I like the choice, as it makes the situation clear and declares that the United States is in the middle of it for ever.
In the meantime, television coverage continues to focus on the Hamas inspired "suicide by cop" protests on the Gaza border. There, hundreds of people at a time are attacking the border fences, trying to enter Israel for violent purposes. What nation in the world would not protect a border from such invasion, and with live fire if necessary? If thousands of people along the Mexican or Canadian border started launching fire bombs into American fields, planting bombs along the border fences, and tried en masse to breach the fences in an organized attack, wouldn't the ICE border control agents have to use their weapons? Wouldn't they use tear gas first, which issuing clear warnings? Wouldn't they use fans to blow away smoke for clear view? Wouldn't they fire warning shots? Wouldn't they have to defend the territorial integrity of the U.S. with live fire if none of that worked? They rules aren't different just because it's Israel.
The Palestinian cause needs to return to the negotiating table. This bloodshed is their plan, and their purpose. Israel must hold fast, even as it loses the publicity war to protect its people.