If there is collision between the president and congress, can congress restrain the President in foreign policy making?
The president is the foreign policy leader for the United States with an important political, military, and economic role in the international arena.
The notion of checks and balances might play into the question. The President has the authority to negotiate treaties with foreign nations. The check enters into the equation in that the framers trusted Congress with the ability to ratify those treaties that have been negotiated. It becomes politically infeasible for the President to negotiate a treaty that is already understood as something that Congress is going to automatically shoot down. While the President might disagree with Congress (invoking the "collision" notion from the question), it becomes in everyone's political interest to understand that no disagreement can prevent the business of government from being done. If this results, everyone loses. While collisions of values might be present, the President and Congress end up fully grasping the concept that the both branches have to work together in fully recognizing the goals and promises of foreign policy.
I agree with both of the above questions, as they have great specific examples of the power struggle between the two branches. I wish to add, however, what is really in my opinion the most effective tool Congress has to restrain foreign policy: the power of the purse, or the budget.
While the Constitution designates foreign policy as an area of the Executive, when we say foreign policy we often mean wars, or foreign aid, military aid, etc. In the case of the Iraq or Vietnam Wars, for example, Congress could end those wars immediately simply by refusing to write any more checks to fund them. The President has a very limited amount of discretionary funding to spend as he sees fit, and certainly not enough to wage a major war, so he depends on Congress to keep paying the bills, and there is no Constitutional requirement that they continue to do so.
The Congress can restrain the President to some extent, but only in certain circumstances.
For example, only the Senate is able to ratify treaties so if a president negotiates a treaty and the Senate does not like the treaty, it will fail. This happened to Woodrow Wilson's attempt to get the US to ratify the Treaty of Versailles and join the League of Nations.
Another example is that Congress can make laws preventing the president from doing something in terms of foreign policy. In the 1980s, Congress made it illegal for anyone to try to help the Contras in Nicaragua and this limited Reagan's ability to conduct the foreign policy that he wanted.
In general, though, the president has by far the most power. The Congress has passed the War Powers Act, but it is not clear if it is constitutional and can be enforced.
There are many instances where the president is bound by law to obey Congress, though there have been substantial assaults on that part of congressional power. In the War Powers Act, the president originally gained some ability to take certain actions without Congressional approval in emergency situations. This has been used a number of times to justify military action without congressional approval. Sometimes that approval was sought and gained after the fact, sometimes not at all.
In recent years, other pieces of legislation have also changed the way the power of Congress to check the president is used or not used. The Patriot Act changed some things and the Bush administration tried very hard to get a great deal more power than they had.
In the end, if there is a huge collision between the two, Congress has the ability to impeach the president but this can generally only be done if he has done something illegal. The political will to do this may also be gone from our government these days as it is so important politically not to make too big of an enemy out of any one group of power holders.