Rambam writes (Hil. Chanukah 3:1) that the bnei Chashmonaim hakohanim defeated the yevanim and killed them and saved Yisrael from their hands and they established a king from the kohanim and the monarchy returned to Yisrael for over 200 years until the second [Temple's] destruction. From this formulation, Rav Yoshe Ber Soloveitchik explained (see Harerei Kedem) that the Rambam held the Chashmonaim acted properly in assuming the throne. However, the Ramban, on thepasuk Lo Yasur Shevet miyehuda (Breishis 49:10) says only shevet Yehuda could be king and the Chashmonaim were punished in assuming the throne and as a punishment they were killed out to the degree that our Gemara says Kol deamar midibeis Chashmonaim Kaasina Avda Hu.
The Chashmonaim line began with Yochanan the Kohen Gadol (abbreviated KG) who was succeeded by his son
Yehudah Maccabee who was KG and king who was succeeded by his brother
Yochanan KG, followed by his brother
Shimon king and KG, followed by
Yochanan Horkynus, king & KG who became a tzeduki after 80 years as KG (see Rashi, Avos 2:4). Followed by
Aristobulus. His wife was Shlomit, sister of Shimon ben Shattach (who was either Nasi or Av Beis din - see Rishonim on Makos 5b) Side point: why does R. Chaim Kanievsky not hold of the name Shlomit (or Shira) to the degree he makes them take a new name? Why isn't it a good name? What will chas veshalom happen is if a woman whose given name was Shlomit and she received a get from her husband and her name on the get was not Shlomit, the get is pasul and if she remarries her children will be mamzeirim! That's much worse than someone having the name Shlomit, isn't it? Aristobulus died without children, and was succeeded by his brother
Yanai, king and KG. Before he became KG, he married Shlomit according to the laws of Yibum, which was muttar for him to do since he wasn't KG yet. Yannai had two sons, Horkynus and Aristobulus.
Shlomit succeeded Yanai as queen with Horkynus as KG. After Shlomit died, Aristobulus became king. He later took over as KG from his brother. Horkynus deposed Aristobulus after he was convinced by Anitpater that Aristobulus planned to kill Horkynus.
During Yanai's reign, Yanai captured Eretz Edom and many of those people converted to be avadim. Antipater was one of these people. An eved. His children included Herod (Hordus), Paziel, and daughters Salome and Shlomit.
Shmuel said Kol deamar idibeis Chashmonaim Kaasinam Avda Hu because in Bava Basra 3b the last of the Chashmonaim who was married (probably against her will) to Herod, killed herself. Jospehus identifies her as Miriam, daughter of Alexander & Alexandra, and Alexander was the son of Aristobulus, the son of Yanai.
Herod and Miriam had two sons, Alexander and Aristobulus, and two daughters, Salampsia and Cyprus. (I'm switching to bullet and number lists to keep things less confusing. Bullet lists are for siblings (same generation) and a new number indicates another generation.)
1. Children of Herod & Miriam (Herod married his children to his siblings' children)
- Salampsia, married to Paziel, son of Paziel, brother of Herod
- Cyprus, married to Antipater, son of Salome, sister of Herod
- Aristobulus, married to Bernica, daughter of Shlomit, sister of Herod
- Alexander - no one important to us
- Salampsia & Paziel had 5 children: sons Antipater, Herod, Alexander and daughters Alexandra and Cyprus
- Cyprus & Antipater - no one important to us
- Aristobulus & Bernica had a son Aggripas I.
Here ends our history lesson.
Now Aggripas is important because Sotah 41 says Aggripas stood during Hakhel and he was praised by the chachamim, but when he read the pasuk "lo suchal lases alecha ish nachri" his eyes filled with tears and people (it's not clear if they were the chachamim or not) told him don't fear, Aggripas, you are our brother, for which statement, the Gemara tells us, the Jews were punished. Which Aggripas was this? If it was Aggripas I, his mother was Bernica, daughter of Herod's sister Shlomit, whose father was an eved. If it was Aggripas II, his mother was Cyprus bas Salampsia bas Miriam, the last of the Chashmonaim, so he was descended from Jewish mothers.
Rashi says this Aggripas was Aggripas II "in whose time the Mikdash was destroyed." (Tosfos in Sotah therefore explains Achinu ata that his mother was Jewish but because his father was not he shouldn't have been king.) Tosfos Yevamos 45b s.v. Keivan must hold it was Aggripas I because Tosfos says he really was an eved and he wasn't really achinu atah, he was only achinu in the sense that eved is obligated in some mitzvos.
As I heard from my Rebbi zt"l which he looked up in Josephus (obviously the last part about which Agrippas wasn't in Josephus!)