What's your thinking on why Oswald let almost all of his 'savings' and his wedding ring? Surley not the action of a normal husband setting off to work.
I'm not even sure he actually left his wedding ring, but even if he did, he might will have believed his marriage was over after Marina refused to move back in with him.
As for the money, I don't know it was "almost all of his savings" and neither do you. A father leaving money to provide for his kids doesn't seem unreasonable to me.