What could have been done to prevent the deaths?

The Montagues and Capulets should not hold grudges against each other and apparently, the deaths would not exist.
The Cause:
Tybalt may not have to be that hot-tempered if there were to be no grudges..His hot-temper had resulted in Benvolio's death... This is the chain of 2 deaths as Romeo, being willingly to avenge Benvolio, killed Tybalt. This eventually leads to the unbalance in the Capulets,especially in Juliet's marriage. After Lord Capulet have found out , he gained negative beliefs in Romeo and of course, definitely objected towards Juliet's decision to marry him. Lord and Lady Capulets insisted on following towards their arrangements to marry Paris.. Getting more and more rebellious as hatred arouse, Juliet left her home...Juliet chose to kill herself rather than to marry Paris.She faked her death by accounting to a mixture of poison, which rests her body with coldness and hardness..People would think she is dead...Romeo, on the other hand, escaped his banishment and felt really anxious about the news... He killed Paris as he sees him... Romeo, thought that Juliet was really "dead", he drank the poison as he suicided.. Nobody notifies him as there is an infectious disease roaming around Verona... Having realized about Romeo's death, Juliet, this time picked up Romeo's knife and stabbed herself... She was left breathless...

Would and Should your character have done anything differently?

In my opinion, Yes he should have the responsibility to guide his Juliet well... Lord Capulet must be decisive and to either make a choice whether to marry Paris or Romeo.. As Romeo was being really loyal towards Juliet and Juliet felt promising towards Romeo, he should have let her daughter marry him...On the other hand, if he wants Juliet to marry Paris, he must have the ounce of dare to try to encourage her daughter to marry as MARRIAGE could not be forced... If he has failed, then he will let her marry Juliet... It is better rather than chasing her out and not recognizing her as her only daughter... He was being very irresponsible really...