Don't eat him! Eat the cake instead! It's Yarne's Birthday and he's one year closer to extinction.
Anyways, Yarne. For some reason he doesn't want to inherit his mother's Wyvern Rider class tree, opting instead for the Barbarian class tree. He does however get his mother's useful Thief class tree and significantly less useful Taguel class (which barely loses out to Villager for the title of worst class in the game). Still, to compensate for the lackluster class, his mother has one of the best stat cap modifier sets in the game with a sizable +3 in Speed, a +2 in both Strength and Skill, and a +1 in Defense which means that she's getting a positive stat cap modifier in her core combat stats, and she only pays for it in Resistance. Yarne will get all that, plus whatever his father has going for him, and an additional +7 that all children get distributed amongst their 7 stats on top of that. Unfortunately this all comes with a price, and a hefty one at that. With the Taguel class comes permanent association with the Beast classification and a perpetual fear of Beast Killers. Moreover, the Taguel class sucks since its best caps are mediocre Skill and Speed scores and even with Beast weaknesses being a common thing, having to be saddled with a 1-ranged unforgeable weapon just to use Beastbane makes it worthless. But even worse is that his mother has neither of the two female exclusive class trees which means Yarne will miss out on being a member of the Galeforce or even the Dual Support+ Brigade. This means his mother should prioritize the class that Yarne will not inherit, Griffin Rider for either its Deliverer or Lancebreaker skill for either enhanced move or a means of counteracting his perpetual weakness.
His best choices for father would be Lon'qu (to maximize his Speed and Skill modifiers as a +7 in Speed means that even as a Wyvern Lord, Yarne will be faster than most classes, and he'll have a juicy +6 for skill activation rates, and with either a Speed or Skill focused Avatar as a wife, Morgan could achieve the highest Speed or Skill cap modifier possible respectfully, and on top of all that he'll have access to Swordmaster for Swordfaire, Astra, Avoid+10, and Griffin Rider to enable access to the +3 Move from Movement +1/Deliverer combo), Virion (for Wyvern Rider access, Archer access in case his +5 Skill modifier isn't enough to hit everything that moves, a solid +2 Speed for a +6 Speed modifer, and Mage access to round out his 9 class inheritance), Stahl (his juicy +3 stat cap modifier total will go great with Panne's +4, his +2 Strength and Defense modifiers round out Yarne fantastically, and his 8 class inheritance includes the Cavalier, Myrmidon, and Archer class trees), and Ricken (for maximum horsing around). Yarne himself is also the second best husband for a Female Avatar (next to Chrom) due to the aforementioned max/near max possible Skill/Speed for Male Morgan to go with his Aggressor/Galeforce/Limit Breaker/Whatever Faire he needs to rock and/or roll/and an attack boosting skill like Ignis/Astra/Luna/possibly Vengeance (and all for the price of Taguel access and permanent Beast Killer/Rapier/Noble Rapier weakness).
Basically, Yarne has the stats, but needs the classes to be good. Unfortunately, as physically oriented as Yarne's mom is, it leaves Yarne with serious gaps in his repartee that drag his performance down in the postgame and challenge DLC and no father can really fix them (not even a Male Avatar; though he helps a lot with Rally Spectrum and Defense access to go with his Rally Strength).