Do you think a marriage between Jace and Helaena and a simultaneous marriage between Aegon and Baela would have been able to stave off the Dance of the Dragons or at least avert it in that generation?
Absolutely not. From the moment Alicent gave birth to her sons, the queen and the green faction wanted Aegon and his brothers to succeed their father ahead of Rhaenyra. Years before Jacaerys was born, Alicent and her father were lobbying Viserys to change his decision on the succession - so much so that Viserys sacked Ser Otto as Hand in 109 AC, five years before Jacaerys’ birth, with the declaration that Lyonel Strong, his new Hand, “[would] not hector [him]”. Gyldayn had already identified the “queen’s party” and the “party of the princess” as extant following Otto Hightower’s termination, and named them with their familiar color designations as of the tourney of 111 AC. For two decades, these parties deepened their mutual antagonism: the Iron Throne was a zero sum game, its seat only big enough for either Aegon or Rhaenyra alone. If the polite and very transitory fiction of the king’s loveday could not change that reality, no amount of cross-factional marriages would either.
Too, such a marriage between Jacaerys and Helaena would require the green faction to acknowledge the legitimacy of the former - a point the green faction, consistently, vehemently, and violently denied. Gyldayn repeats not only Alicent’s sniping comment to Laenor after Lucerys’ birth - that if he, Laenor, kept having children with Rhaenyra, “soon or late, you may get one who looks like you” - but also the “article of faith” amongst the greens that “the father of Rhaenyra’s sons was not her husband, Laenor, but her champion, Harwin Strong”. Alicent’s sons had certainly learned by 120 AC to denounce Rhaenyra’s sons as “Strongs”, with Aegon merely shrugging that “[e]veryone [sic] kn[ew]” about the boys’ extramarital origins just to look at them. No matter how true the accusation probably was, and no matter how firmly Viserys attempted to shut down this particular line of questioning, the green faction was never going to agree to a marriage between Alicent’s only daughter and an ostensibly Velaryon prince the greens held to be a bastard.
Indeed, what we see of the marriages and betrothals among the children of these factions IOTL was a desire not to merge these groups together but to emphasize mutual isolation from each rival faction. Alicent may have contemplated marriage between her Aegon and Rhaenyra (less a goodwill gesture to the latter and more, I think, a guarantee of Aegon’s accession and reliance on patriarchal expectations to promote him eventually as sole ruler), but when Viserys shut down that idea, Alicent’s solution was to marry Aegon to Helaena - another way of emphasizing Aegon’s role as heir to the similarly incestuously married Conqueror (and, by extension, Aegon’s right to take the Conqueror’s throne). Rhaenyra, for her part, betrothed her eldest sons when the boys were little more than toddlers - early even by Westerosi standards, and a clear indication both that Rhaenyra had aligned herself with the Velaryon-Targaryen branch of the family and that her sons were not available for the nuptial schemes of either the green faction or the king (since Rhaenyra firmly held out her sons as Velaryons, nevermind the antipathy of the greens as I mentioned). Far from either faction being willing to use the traditional tool of dynastic marriage to make peace, both the blacks and the greens dug themselves in more deeply to their positions in the decade before the Dance.
