We headed toleft for Tokyo in a minibus with my father's coworkers.

"headed" is probably a good translation of "向かう" here, but it puts emphasis in my mind of the journey in the minibus rather than the trip to Tokyo, like something will happen between leaving and arriving. The "left" I suggest here just brings to mind an image of leaving. I also thought of "went" which emphasizes the arrival.

After that, we enteredWe arrived at a certain building and, as instructed (by whom?), sat down to pray with my father, but I couldn’t tell if my father was actually praying.

I didn't feel like a specific enough action had been specified to use "that" here. If we assumed "that" referred to being overwhelmed with excitement, it would imply that at the time when you entered this building you were no longer excited. If "that" refers to arriving in the city, I feel it's more common to say the final destination as where you "arrived" than the city.

(by whom?): The sentence is fine as is, but who did the instructing is unspecified. It's maybe not hard to guess, but it's not as common to say "as I was told" in English without adding "by ___" as it might by to say "言われる" in Japanese without a "〇〇に".

My father asked me if I wanted to go to Tokyo, and so for the first time, I was goingent to visit the city.

After that, we entered a certain building and, as instructed, I sat down to pray with my father, but I couldn’t tell if my father was actually praying.

'A certain building" in not incorrect, but it sounds odd in this context.

In front of us were people who seemed to be in a state of possessioned.

My father asked me if I wanted to go to Tokyo, and for the first time, I was goingent with him to visit the city.

It was 260 kilometers from my home.

Optionally, you could change “from my home” to “away.”

After thatOnce we arrived, we entered a certainthis building and, as instructed, I sat down to pray with my father, but I couldn’t tell if my father was actually praying.