Trotting between the two markers in Sa`i should be done in all laps

Yes, one should walk fast between the two markers in all laps of Sa`i, from al-Safa to al-Marwah and from al-Marwah to al-Safa. 

Ibn Qudaamah said in al-Mughni (10/236), when describing Sa`i between al-Safa and al-Marwah: 

It means coming down from al-Safa and walking until you are level with the marker, which is the green mark that is attached to the corner of the mosque. When you are about six cubits away from it, you should walk quickly until you come in line with the other marker, then you should stop trotting and walk (normally) until you come to al-Marwah, then stand to face the qiblah and say du’aa’ as you did at al-Safa. … Then come down and walk in the place for walking, and trot in the place for trotting. End quote. 

The scholars of the Standing Committee for Issuing Fatwas were asked about that and said: 

Yes, it is the same when going from al-Marwah to al-Safa as when going from al-Safa to al-Marwah, because the Prophet (peace and blessings of Allah be upon him) did that, as is proven in the saheeh ahaadeeth. 

And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 

Standing Committee for Academic Research and Issuing Fatwas 

Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allah ibn Baz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allah ibn Qa’ood.