Dear ViceRoy!
Your question about Cartage origin & his "blood relationship" with Phoenician civilization raise more interesring aspect of all Rome History - issue of her "Destination".
It's really complex & weird story. I would need to make 5-6 "lessons" for its complete revealing, but it is my shortened & abridged version.
I think you know that Rome was founded (by legend) by Greek colonists in really ancient times. Later Greek' influence was completely shadowed by local Latin culture tradition, then we have two parallel sets of legends of Rome founding (i.e. Enei story, & story about Capitoly Wolverine). Legend of Latin origin was more important for Rome citizens, but Enei story kept itself as weird rudiments in Rome religious teachings & beliefs. One of the most important source of these teachings is "Book of Sybil" that we got by fragments & as narrations from different Rome authors.
First of all - you must realize that Rome' Gods weren't equal to their Greek' counterparts & had completely different meanings & usage (their "convergence" took place later in Early Principate times under Augustus civil & religious codex). Main usage of original Rome Gods kept in... Astrology. Yep, Astrology meanings is more corresponding meanings of Rome gods, then their Greek analogues. (By the way, Greeks were more "materialistic" in their beliefs & used really uncommon fpr us naming of planets - Phaeton (Jupiter), Phenont (Saturn), Wesper & Eosper (sunset & sunrise Venus respectively) etc.)
Most important for Rome God was - Virtus, who got great resemblance to modern Mars, but had more meanings. In some sense Virtus was "Soul of Rome" & had really surprising correspondings in human body to Head &... nether parts (i.e. Mars of modern Astrology had influence on Head (Aries) & Reproductive system (Scorpio) in human beings. Then all Rome culture had subservient usage for pleasing "head &... other" needs. It brought real big affection of Early Rome to teaching of all sorts & great importance of lupanars (whore-houses), pornography & else for Rome culture development. (By the way - this great "affection" to "carnal pleasures" was most important issue to name Rome as "barbarian", "rude" & "vulgar" community then any other means by her neighbors.)
In any case - "Head" functions of Virtus was considered more important for Early Rome then anything else, & "Aries" aspects was considered more important then "Scorpio" aspects. Rome priests taught Rome people that most important thing for Rome prosperity is "Celestial Harmony" between Rome Virtus & other Gods. (Really sound idea for Astrology

.)
Aries has two most "Harmony" aspects - to Leo & to Sagittarius. You must realize that Rome didn't know modern associations with Leo & Saggitarius & considered them as "Sun" & "Jupiter" principles manifestation. "Sun" manifestation was linked to Greek God "Apollo" & his Soul was known as Noos (i.e. Knowledge) & "Jupiter" manifested as ("Power" & "Prosperity"). Then - Total Harmony by Rome beliefs could be reached by "Trinity" principle: Virtus (Willpower & Management), Noos (Knowledge & Forgiveness) & "God Blessing" ("Power" & "Prosperity" was prerogative of Early Rome Kings & lately - Senate as whole, or Consuls later (this is a Reason for Princeps having "Divinity" attributes in Principate times).
Virtus was Rome itself & Noos... Noos was Greece as whole.
By other words Rome from moment of her founding saw on Greece as - necessary part of Rome society & main reason of Rome existence was creating "Eternal marriage" with Greece. (Rome was considered as "Second Celestial Man" & "Greece as Second Celestial Woman"). Rome had really strong belief that any state is resembling human being & its "Destiny" is creating good sound family, raising offsprings, building "house" & at last - dying. (It is really strange thing - Rome phylosophers discussed question "what it will be, when Rome will died" without any winch, when more modern phylosophers meet idea of dying of any existent states with fits of hysteria

.)
(Check History - when "Man" part of Unity, known to us as Imperial Rome, died - his "Woman" part, known to us as Byzantium outlive her "Celestial Husband" by one thousand years! It seems - these Rome phylosophers - knew issue they talk about!

)
By the way - you could see that Rome priests saw Rome as "Second Celestial Man" but who was "First"?
Rome religious Dogma was: It began in really ancient times. Possibly there was other "Celestial Pairs", but we didn't know anything about it. First known "Celestial Woman" was Egypt. "Women always come into worlds earlier then Men, due to their Nature & always outlive their spouse". First known "Celestial Man" was Phoenicia (or "peoples from sea", or "Peleset" tribes of Bible, or Semito-Hamite tribes of modern meaning) & Chaldea (i.e. Babylon). "First Man layed First Woman by force & created First Celestial Marriage". Known "House of this Martriage" for Rome was Pyramids, Baalbeck & Hanged Gardens ruins & etc.
After really long time after there was appearance of "Second Woman" - Greece. When this "Woman" - realize itself & her Destiny "she decided to destroy First Marriage", because "she needed World for her own Marriage, her own House & her own offsprings". She born Alexander the Great who completely destroyed "First Man" - (Phoenician city-states & post-Babylonian state of Persia) & subdued "First Woman" making it - "Greek' slaverine". But "Greece was a Woman, but no one woman can make her work properly".
"Seed of First Man" in form of Cartage kept itself alive & now Life dangerous for "Second Woman" again. Then - it's job for "Second Man" - to destroy Cartage & any "seeds of First Man" completely. (This religious teaching was reason for really harsh attitude to Cartage, Phoenicia, ancient Jews & - later to Christians from Rome inhabitants.) Rome Destiny was "complete Cartage destruction", "laying Greece & making her Rome loyal Wife" (it was reason for really gentle attitude to Greece population after occupying this country by Rome forces), "breeding offsprings with Greece (by the way rome people believed that "husband - master of his house, but wife - master of house interior" (this was a reason for fast adaptation by Rome of Greece cultural tradition - "husbsand must try to please his woman by living in her way"). Etc.
By the way - in this religious teaching we got seeds of next most important Rome Civil War - between Anthony & Octavian. It was said - Old woman tries to steal our Man Power from Rightful Wife, then this old hags must be destroyed". (Somebody tried to pretend that "Old Woman" is Cleopatra< but if you realize that "Old Woman" is Egypt - you understand really bitter taste pf this war & reasons of Anthony soldiers - don't fight for Cleopatra (Egypt) cause!)
About Rome cavalry. You must realize that Horse was power status sign in any ancient society. In Rome number of Patricians families couldn't exceeded - 300 due to Rome had 3 "tribes" & 30 "curies". Then all other Patricians families (i.e. younger offsprings of usual Patricians) became Plebs families - i.e. became equal to slave offsprings. It was wrong thing for any conscience Rome citizen< then Patricians didn't like to underline this difference - it was considered really rude to ride before crowd on horse< - then many patricians having horses never used it. Name it as sort of "reflexia" or "aching conscience" for most noble Rome Patricians.

But it was reason of really weak condition of Rome cavalry!
Sincerely yours, Alex.
P.S. Do you like some Fables?
I tell you one (keep in mind all text upper).
Fable is omitted.