Let the mass of the girl and her twin sister be m and their velocities after separation be v

Momentum before separation = 0

Momentum after impact = mv

By the law of conservation of momentum:

Momentum before they push apart = 0 = momentum after they push apart = mv

Therefore: 0 = mv

However if they are of unequal mass the person with the greater mass will move off much more slowly after the initial push.

Let the mass of the girl be m, the mass of the man M and their velocities after separation be v and V.

Momentum before separation = 0

Momentum after impact = mv

By the law of conservation of momentum:

Momentum before they push apart = 0 = momentum after they push apart = mv + MV

Therefore: 0 = mv + MV and so mv = - MV v = - [M/m]V

If the mass of the man is double that of the girl she will 'recoil' at twice his speed.