What would cause two stars to collide? What does it take for a whole planet (as massive as Jupiter) to change trajectory?
The main mechanism that would make two stars collide is gravity. This depends on several factors, some stars may wander through space and end up being attracted by the gravitational field of another star, from there, one star begins to orbit the other.
But the most common are collisions in clusters of stars, because in a star cluster the stars are very close together, especially in globular clusters.
Collisions of young stars may also occur, as most of the stars are born close to each other in clusters. Many stars are binary, formed together, but in some cases before they evolve they may end up colliding.
In the universe both collisions of active stars can occur, as can collisions of white dwarfs, neutron stars and black holes.
The orbits of the planets are determined by the gravitational pull of the Sun, so it would need some very extreme force to cause the orbit of a planet to change its trajectory, perhaps if some planet or star enters our solar system, or when the Sun goes through changes and become a white dwarf in about 5 billion years.