This is what special relativity is all about..
In special relativity you cannot simply state that particle 2 is moving at c+c=2c in a reference frame where particle 1 is at rest.
Speeds add like this (easily found in wikipedia):
$$v_2^' = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$$$v_2^{'} = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$
i.e. the speed of particle 2 $v_2^'$$v_2'$ in a reference frame where particle 1 is at rest is
$$v_2^' = \frac{c+c}{1+1} = c$$$$v_2^{'} = \frac{c+c}{1+1} = c$$
you cannot move faster than at the speed of light in the vacuum.
