My question is should we view the tragedy of Karbala moreso as a praise of the Ahlul Bayt or should we view it in terms of its broader messages (such as justice and imaan and oppression) without so much focus on the Ahlul Bayt? My understanding of Karbala was not with a focus on the ahlul bayt, but of the universal ideas of divine justice and truth. Also how much should we use the wasila of the Ahlul Bayt in dua?

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As far as the tragedy of Karbala is concerned, this is the fact that the sacrifices of Imam Husain (a.s) and his family member and his companions was beyond the the imagination and this proves that Imam Husain (a.s) was divine leader and Ahlulbayt of Hy Prophet (saww), so knowing about karbala not only strengthen ones faith in Ahlulbayt but it is also important to understand true successor of Holy Prophet (saww).
As you asked about Wasila, Quran says:

يَا أَيُّهَا الَّذِينَ آمَنُوا اتَّقُوا اللَّهَ وَابْتَغُوا إِلَيْهِ الْوَسِيلَةَ وَجَاهِدُوا فِي سَبِيلِهِ لَعَلَّكُمْ تُفْلِحُونَ

O you who believe! be careful of (your duty to) Allah and seek means of nearness to Him and strive hard in His way that you may be successful.(5:35)
Therefore ofcourse we can make them Wasila in our Duas as they are closer to Allah(swt) other than any individual.