After conquering Dorne, if Daeron named the then-current Martell Prince or some other Dornish lord (ex.Yronwood) Lord Paramount of Dorne rather than making Lyonel Tyrell ruler, do you think events could have turned out differently?

A combination of conquest and incorporation via marriage can work in Dorne, we can look at Nymeria for proof of that. So I could see a situation in which the Prince kneels, Daeron takes a Martell bride to cement his legitimacy, and Dorne is incorporated. 

However, I do think some things have complicated that scenario. First, the First Dornish War created a legacy of Dornish nationalist resistance against Targaryen brutality which will be hard to overcome. Second, Daeron’s whole purpose for waging war in Dorne is to use military conquest to restore royal authority by being able to dole out rewards to his followers – the king as “ring-giver.” So the more lightly he treads with the Dornish to avoid resistance, the less he succeeds at his ultimate political goal. 

Really, the only way I could see it working is if you have a significant migration of Westerosi into Dorne, with the second sons of the Reach and the Stormlands etc. marrying into the population as well as occupying the castles.