There is also a companion to part 2 aka Roma Aeterna. The introduction to the companion to Roma Aeterna says:
“Hans Ørberg’s Rōma Aeterna ……begins with Ørberg’s own admirable prose (Caps. XXXVI to XL). Cap. XXXVI helps the instructor assess student strengths and weaknesses. This chapter effortlessly brings students back to their Latin after the inevitable break from Latin over summer or winter vacations. It also introduces critical new syntax. Students first learn, for example, about subordinate clauses in indirect discourse in Cap. XXXVI. Caps. XXXVII–XL offer a prose retelling of the early books of Vergil’s (Pūblius Vergilius Marō) Aeneid. These chapters are a good bridge from Familia Rōmāna to the unadapted selections in Rōma Aeterna. A prose narrative, instead of verse, is prudent: although students are often enticed into reading more Latin through the offer of poetry, without a solid foundation in Latin prose, they will not be able to appreciate the special voice that Latin verse offers. The prose is in part closely modeled on Vergil’s language, interspersed with verse excerpts from the Aeneid.
Caps. XLI–XLV introduce the Roman historian Livy’s (Titus Līvius) ab Urbe Conditā. Ørberg’s adaptation enables the student to become gradually accustomed to Livy’s prose style. The Latin grows increasingly less adapted until Cap. XLV.222, after which the student reads unadapted—although not unabridged—Livy. Cap. XLV is the transitional chapter, and, if one chapter is to introduce students to unadapted ancient texts, it is a good place to start. While the predominant author for Caps. XLI to LI is Livy—either in his own words, Ørberg’s adaptation, or the periochae (later summaries of the lost books of Livy’s history)—we are also introduced to other authors who have contrib-uted to our understanding of Roman history: Eutropius (Caps. XLVI and LIII), Aulus Gellius (Cap. XLVII), Cornēlius Nepōs (Cap. XLIX). While the styles of these writers differ from Livy’s, the change from chapter to chapter will not present any obstacle to the reader. At the end of Cap. LI, however, we are introduced to Sallust (Sallustius Crīspus), presented, as Quintilian advised, after the reader has a good amount of experience with Latin prose. Sallust is, as Quintilian warned, more difficult to understand. Some rudimentary remarks, not only about individual style but also about generic expectations, can be found in the section on style at the end of this introduction as well as in the Points of Style sections in individual chapters. “
You may also find this helpful also from the companion:
“ Rōma Aeterna was composed as a continuation of Familia Rōmāna. Although some readers will want—and have the necessary time—to read the text cover to cover, the companion is designed to facilitate selection. A good deal of repetition in the reading notes is one result: the companion does not take for granted that everyone has read and remembered everything that went before, and the notes will generally reference the chapter (of Rōma Aeterna or Familia Rōmāna) where a concept is discussed. Since the two parts of Lingua Latina (Familia Rōmāna and Rōma Aeterna) were written sequentially, chapters are referred to by number alone. “
So it’s your choice whether you read any, some or all of part 2. But if you decide to read something else you will need to learn the grammar covered in the early chapters of Roma Aeterna. If you have found familia roma helpful then continuing onto Roma Aeterna seems like a good plan. Whether you read all of it will depend largely on whether you are interested in the texts offered or want to go your own way.
Hope this is helpful