Hayashi san, who was 82 years old when she opened the store, makes dumplings with her experienced hands.
and I was wondering whether to read 開店時【かいてんとき】 or 開店時【かいてんじ】
Like the English verb open, 開店 is ambiguous between start a new shop and open in the morning. (For the latter, usually most shops open in the morning, I suppose, but it could be in the evening or at night. Anyway for the first time in the day.)
開店時 in the first sense is read as かいてんじ.
開店時 in the second sense can be read both as かいてんじ and かいてんどき of which my impression is that かいてんどき is more common.
The 開店時 in the question is in the
second first sense, so it can be read as both かいてんじ.