LotR -- Book 6 - Chapter 3 - Mount Doom

[Firefoot]

But if Gollum was wrong to take the life of Deagol to get what he wanted, & Eru killed Gollum to get what He wanted how would that be different?

It's entirely different. For one thing, Smeagol's murder of Deagol was just that: murder. Smeagol is in now way in the right. He wants something Deagol has, so he kills him for it. On the other hand, Eru, the Authority, causes Gollum to slip - both just and merciful, not just "to get what he wanted." Smeagol's motives in killing Deagol were entirely selfish, Eru's were not - and Gollum wasn't just a random bystander, either. Gollum had his chances at redemption, but he chose not to take them and continued on his own selfish quest to get the Ring back. He was offered forgiveness and mercy, but accepted neither. Eru's "killing" of Gollum was both just and merciful - mostly to Gollum, but also to Frodo and to all of Middle-earth. And it's not like Gollum wasn't acting of his own free will when he took the Ring and was dancing around with it.