The face to face interaction of two dust acoustic solitons with adiabatically trapped ions and Maxwellian electrons is investigated in a dusty plasma. The extended Poincaré-Lighthill-Kuo (PLK) technique is used to derive a pair of trapped nonlinear partial differential equations with fractional nonlinearity. Interestingly, unlike the untrapped case, the interaction and the phase shifts of the dust acoustic solitons cannot be obtained analytically for the trapped case and, therefore, evaluated numerically. This leads to the important finding that the phase shift depends upon the velocities of both the solitons. Furthermore, the number density of electrons and the temperature of ions are found to affect the phase shift of the colliding solitons. The present investigation is carried out for the parameters pertaining to the Saturn’s magnetosphere, however, the results presented here are general and can be gainfully exploited to comprehend the interaction of solitons in space and laboratory applications of dusty plasmas. •The face-to-face interaction of two dust acoustic solitons with trapped ions is investigated.•The PLK technique gives a pair of trapped Korteweg de Vries equations with fractional nonlinearity.•Unlike un-trapped case, interaction of solitons cannot be obtained analytically, so analysed numerically for the trapped case.•Furthermore, phase shifts of the solitons depend upon the velocities of both the solitons.•The plasma parameters pertaining to the Saturn’s magnetosphere affect the phase shift of colliding solitons.