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The Middle East peace process is on the brink of collapse due to a row over a United Nations report condemning Israel of war crimes. A brink is the point in time when something very good or very bad is about to happen. If nations or people are having a row about/over something, this means they have a very serious disagreement over an issue.
Unfortunately the UN report causing the row threatens to sink the peace plan. Normally, this verb describes a boat or other object that falls to the bottom of a body of water, but here it means to make worse.
In this dispute, the UK is refusing to back Israel over the Gaza offensive. If you back someone or something, you give your give support.
If the negotiations collapse, this could scupper President Obama’s Middle East plans. To scupper is a naval term meaning to deliberately sink a ship by letting water in. In informal British English, to scupper means to spoil someone’s plans or hopes of success.