Is there a way to Bring to Life my Lucky Clover and still cast Animating Faerie?
Nope, your analysis of what should happen is spot on.  Short of having another card or ability to use, there's nothing you could have done.  You'd need to have a way to stop the triggered ability (Stifle), counter the copy or have another legal target.
Silly as it might seem, sometimes normally beneficial effects have detrimental edge cases.  That's just part of Magic.