Is what I did correct, praying Asr after Maghrib as a make-up, then praying Maghrib in another mosque after I had led the Maghrib prayer that was established, while you had not prayed Asr?

It is the Muslim's duty to gain understanding in matters of their religion, especially individual obligations (fard al-ayn). The prayer mentioned is invalid for two reasons: changing the intention from Maghrib to Asr, and intentionally saying the taslim before completing the prayer. If your intention was the Asr prayer, then you must repeat it. As for the Maghrib prayer, you do not need to repeat it, as you prayed it in another mosque.