Marriage is NOT indissoluble. There, said it.

Start anything on a falsehood or completely unrealistic premise and the result is a tangled web. 

Congratulations to AnonAJ who recently celebrated 50 years of marriage (I think) and is a shining example of what can be achieved with love, faith, joy and, I'm sure, hard work, self-sacrifice, support and good luck. Her marriage was, is and always will be indissoluble.

But she'd be the first to be compassionate to those for whom things didn't work out. The Hierarchs - and that really is the accurate term for them - loaded burdens on them, stigmatised them and withdrew support. But the Eucharist?!  (And as others have mentioned, they have done this during the abuse crisis and cover up.)

The only reason many of the divorced/remarried hang around is because - as usual - decent Catholics have ignored the Church and ministered informally (non clerically) to such people. 

I'll take my advise from AnonAJ before any Cardinal.