Yes, your understanding is correct. 広い部屋の is not a modifying clause(連体修飾節), but a modifying phrase(連体修飾句). 部屋が広いアパート/部屋の広いアパート is grammatically correct, but actually, it's rarely used.
Google search results
部屋が広いアパート 10hits
(One of them is for an answer in Genki textbook probably as same as you, one is for a different meaning (一人暮らし用に部屋数より、一つの部屋が広いアパートを探しています), two of them are not a modifying clause (部屋が広い!(アパートのような)), four of them are from the same site, thus, the actual result is just three;
もう少し部屋が広いアパートにすればよかったです
部屋が広いアパートに住みたくなった
今より部屋が広いアパートを探すと家賃が高いため)
部屋の広いアパート 7hits
(One is for Genki, one is for a different meaning (三人部屋の広いアパート))
広い部屋のアパート 35,100hits
You can also use アパートがいいです for #1 and #2, especially when you are asked what kind of apartment you are looking for, as in Genki.