What had the people done that was so bad? How can a loving God be angry? Is God's sentence to destroy Israel and raise up a new nation through Moses justified?
See the way I read it, the people did not request to have idols made. Moses was in the mountains with God for 40 days, and the people lost their faith because they didn't have anything in front of them to see (not unlike us). However, Aaron told them to go and get all their gold and Aaron fashioned an idol for them. Howbeit Aaron may not have thought of it as an idol it became an idol. What the people did that was so bad, was they quit trusting in God. God who had brought them through the red sea, God who had provided manna every day for them. God gave us all short term memory.
God can be angry just as we can be angry, it doesn't mean He isn't loving. I love my children but I do get angry with them.
If God had destroyed Israel would it have been justified? I am nobody to judge whether God would be justified. Would it have made a difference to raise up a new nation? Abraham pled for the "lack of 10", however, after Lot and his family were removed and the city was destroyed, Lots daughters got their father drunk so they might have children.