IPA Letter entry formalities

Hello, I already have my IPA letter to collect my student pass. However, I was wondering if with the IPA letter I was able to re-enter the country multiple times. I'm asking this because I'm arriving a few weeks before classes start with my family to travel around the region. Hence, I will arrive at Singapore and stay JUST ONE day, then I will leave to travel; and I will finally re-enter after a few days.

Or do you recommend that I enter as a tourist first (I do not need a visa for visiting Singapore), and then to present the IPA letter when getting back the second time?

As stated on your IPA, it is a one-time entry visa for the purpose of collecting your student pass and starting your full-time classes.
If you enter for any other purpose, you need a separat visa.