If God sends someone to Hell, shouldn't we rejoice He is God and it's His Judgement to send them

This creates a false dichotomy. Either we have to be sad or rejoice when God judges a soul. I don't think humans should concern themselves with God's judgement of others period. That is between them and God I think Jesus made this clear.

I'm not saying my judgement is better than God's, to the contrary I am saying we do not know God's judgement.

We also cannot know what God actually judges, because we are of earth. To presume to know God's judgement is a flaw.