I know that in inertial ( stationary) frames conservation of momentum is a statement that sum of momentum before and after collision is same but what about moving frames? Particularly, accelerating ones?
Would there be a way to change the impulse equation so that it works in such frames? $$\Delta p =\int F * dt$$
Newton's laws obey Newtonian relativity (often called Galilean relativity, but Galileo's statement was not precise and applies equally to Einstein's relativity. Newton's statement was precise). Consequently uniform motion makes no difference to conservation of momentum in Newtonian mechanics.
For an accelerating frame, the inertial force (pseudo force) integrated over time will change momentum. But in collision the amount of time is negligible, so the effect of the inertial force on conservation of momentum in collision would usually be regarded as negligible, meaning that conservation of momentum still holds.
