What a neat project Judy! Here’s what I know if I were to attempt this.
Final resin cure strength is dependent on the resin. i.e. Some resins cure very hard and brittle, others cure soft and pliable. I don’t know that adding fiberglass fibers is going to make the resin stronger. Instead, if you are worried that people would try to break off the ends, I would use a resin that cures a little ‘bendy’. That way if someone does grab it, it’s not going to snap.
However, all that said, at the thickness you are casting, a hard curing resin might be suitable. I would suggest casting a length (no branch necessary) in the resin you are considering. Demold and put it up like you intend to display it. Have friends and family touch it, try to break it, etc. It might be fine…. But if it is a long piece, maybe not.
P.S. I would love to know what you end up doing. Please report back how it goes!