Switching passports/visa

maybe someone out there can give me some advice. i’ll try to explain my situation as clearly as possible.

Before i came to Taiwan two years ago i mailed my canadian passport from calgary, canada to vancouver, canada to get a two month visitors visa from the TECO office. I sent the money order, the flight itinerary, and a copy of my bank statement, as aked by them. standard procedure.

For two years now i have had an ARC from the same employer. That ARC is due to expire November X since i’m not renewing my contract. i have already planned a trip out of taiwan, for vacation purposes, and realize in order to enter taiwan again and find another job, i will have to again get another two month visitors visa.

I also hold an american passport. here is my question: could i, from taiwan, mail my passport home, have dad mail it to the SFO TECO office, (application etc. included), have it sent back to dad (my address in the states), have him mail it to me here, and then return from my vacation on my US passport with the new visitors visa? would i have to have another ticket showing that i’m leaving taiwan after the two month period? i had to do this in canada. i had a stupid one way ticket to hong kong that i never ended up using.