After Doom of Valyria, a century of violence and turmoil engulfed Essos. Volantis, the strongest of the 9 daughters claimed herself to be the successor of the Valyrian Empire and sought to subjugate her sisters by force to revive Valyria.

While initially successful, they were soon facing an alliance of all the Free cities (Except Lorath), Stormlands and Targaryens of Dragonstone (Who joined the war on request of Pentos and Tyrosh).

I can understand the reasons of all the other belligerents.

1. Free cities wanted to remain free of Volantene yoke.


2. Stormlanders were threatened by Volantis' aggressive expansion right across their shores.

But what about the Targaryens? Why would they feel threatened by Volantis or a revival of Valyria 2.0 (sans Dragons) when they had the only dragons in the world? Of course Dragonstone was part of the Valyrian freehold and Volantis may have laid claim to it as successor to Valyria but three dragons would have been more than enough to repel any invasion from the East. Even if Valyria was revived, the Targaryens could have actually forced the new Empire to accept their leadership as the last Dragonlords and the last of the 40 Freeholder families. Not to mention, there'd be a significant part of the population who'd support the Targaryens precisely because of that. But still we see Aegon completely against the idea of the Valyrian resurgence. Not just that, even his heirs were absolutely opposed to a Valyrian revival. I talked about those reasons in some of my previous answers but they just don't convince me entirely for reasons outlined above.

Did Pentos and Tyrosh promise some lucrative deal to the young Lord of Dragonstone to get the Targaryens on their side?

Why did Aegon the Conqueror ally himself with the Free cities when he never showed interest in Eastern politics before or after that war?

It is really not known why Aegon did this, but it seems he did to remove the distraction/threat of Essos so he could focus on Westeros.

Near the end, even the future Conqueror, the still-young Aegon Targaryen, became involved in the struggle. His ancestors had long looked east, but his attention from an early age had been turned westward. Still, when Pentos and Tyrosh approached him, inviting him to join a grand alliance against Volantis, he listened. And for reasons unknown to this day, he chose to heed their call...to a point. Mounting the Black Dread, it is said that he flew to the east, meeting with the Prince of Pentos and the magisters of the Free City, and from there flew Balerion to Lys in time to set ablaze a Volantene fleet that was preparing to invade that Free City.

...

As for Aegon Targaryen, shortly after his role in defeating Volantis it is written that he lost all interest in the affairs of the east. Believing Volantis's rule at an end, he flew back to Dragonstone. And now, no longer distracted by the wars of Essos, he turned his gaze west.

_{The World of Ice and Fire - Ancient History: The Doom of Valyria}

We Do Not Sow Know

It is explicitly mentioned in The World of Ice and Fire that the reasons for Aegon joining the alliance are unknown.

Near the end, even the future Conqueror, the still-young Aegon Targaryen, became involved in the struggle. His ancestors had long looked east, but his attention from an early age had been turned westward. Still, when Pentos and Tyrosh approached him, inviting him to join a grand alliance against Volantis, he listened. And for reasons unknown to this day, he chose to heed their call...to a point. Mounting the Black Dread, it is said that he flew to the east, meeting with the Prince of Pentos and the magisters of the Free City, and from there flew Balerion to Lys in time to set ablaze a Volantene fleet that was preparing to invade that Free City.

_{The World of Ice and Fire, Ancient History: The Doom of Valyria}

However, we do of course know that dragons are not invulnerable and we saw a Vermax suffer a fatality in a similar naval battle.

It is one thing to face a dragon, another to face five. As Silverwing, Sheepstealer, Seasmoke, and Vermithor descended upon them, the men of the Triarchy felt their courage desert them. The line of warships shattered as one galley after another turned away. The dragons fell like thunderbolts, spitting balls of fire, blue and orange, red and gold, each brighter than the next. Ship after ship burst asunder or was consumed by flames. Screaming men leapt into the sea, shrouded in fire. Tall columns of black smoke rose up from the water. All seemed lost … all was lost …

… till Vermax flew too low, and went crashing down into the sea.

Several differing tales were told afterward of how and why the dragon fell. Some claimed a crossbowman put an iron bolt through his eye, but this version seems suspiciously similar to the way Meraxes met her end, long ago in Dorne. Another account tells us that a sailor in the crow’s nest of a Myrish galley cast a grapnel as Vermax was swooping through the fleet. One of its prongs found purchase between two scales, and was driven deep by the dragon’s own considerable speed. The sailor had coiled his end of the chain about the mast, and the weight of the ship and the power of Vermax’s wings tore a long jagged gash in the dragon’s belly. The dragon’s shriek of rage was heard as far off as Spicetown, even through the clangor of battle. His flight jerked to a violent end, Vermax went down smoking and screaming, clawing at the water. Survivors said he struggled to rise, only to crash headlong into a burning galley. Wood splintered, the mast came tumbling down, and the dragon, thrashing, became entangled in the rigging. When the ship heeled over and sank, Vermax sank with her.

_{The Princess and the Queen}