First, I am so sorry that you are dealing with this, particularly with your other family challenges at the same time. I helped my mom manage pension and such after my stepdad's death, so I know up-close-and-personally how hard that kind of loss can make even simple decisions for even very smart people. My condolences.
Here is one way to think of it:
Do you need the money now? If you need the money now, that changes the calculus, and I'd vote for taking the cash and investing it. If you don't need the money now, then I think it is a good idea to view this as more of a safety net.
What is your family/health history? If it suggests that you may live a good long time, I like the idea of waiting to take it at 65, because it makes a very nice safety net. If your expenses are around $60K, then that pension will cover almost 1/3 of your needs when you start receiving payments (because COLA). That's a nice safety net to have.
On the other hand, if your family/health history suggests you might not have a super-long lifespan, you could take it now and invest the $500 or so. That guarantees you personally get some value out of the pension (it's great that they pay out to your heirs, but you matter more). Plus, as long as the $500/mo. is also COLA-protected, that's a decent way to split the difference between having some long-term safety net vs. getting immediate growth from the $$.
FWIW: any decision you make will work out well. I strongly suspect, as someone else noted, that the three options are actuarily the same. So there's no "wrong" decision -- just different versions of better.
