You really have absolutely no basis for the way you wish to approach this:

1. The schedule change happened *before* your brother unfortunately passed away. Had he not passed away, you would've been in the same boat. You're just using his passing to be able to get your money back.
2. Even if you stuck to your original flight, you would have to, as you said, get a new, earlier ticket from Chiang Mai to Bangkok (although, I would've given it a try with a 2-hour window. You could've even tried to get your bags tagged all the way in Chiang Mai, since SQ and TG have interlining. Then your 2-hour window would seem like just a normal transfer.)
3. After your original flight change incident was over, your brother passed away. Naturally, you tried to get home as soon as possible, and of course in order to accommodate that, SQ needed some kind of proof - just remember all the jokes of kids in school skipping homework because a relative "passed away".
4. Being unable to provide proof on short notice, and also unable to wait for SQ to provide any kind of assistance on the spot, you bought your own ticket, which is fine.
5. You were using a bad and incompetent travel agent.

Flight change incident is irrelevant to your case, it's a done deal. You are owed nothing by SQ, especially since you didn't actually take the return flight. You should figure out what the travel agency did.

Your brother's passing would entitle you to a refund of unused portion of the ticket, but *not* for your repatriation on a different flight.

You gain nothing from mixing those two unrelated incidents together, other than weakening your story and your position.

Other than time, your litigation would also cost you money, as lawyers will probably cost significantly more than any refunds or compensation you may get from any of the parties. You have no legal basis for a case against SQ.

I mean, seriously, even if everything played out according to your original plan, what if your TG flight from Chiang Mai was delayed an hour and a half? You'd miss your connecting flight in BKK, and then what? You'd sue TG for having a flight delayed?

Use the collective wisdom of FlyerTalk to work out the best way to sort it out with SQ, not to find ways to justify your intent to sue everyone involved. People on here can help you to clarify your case, find the right information, and present it to the airline in the format the airline expects it. Throughout the multiple threads, you've been given some good guidance on ways to approach the matter (and to untangle your stories). Stop ignoring it.