Yes you may. I have 3 (8-9-12). I don't "trust" them to not eat candy that I said they shouldn't eat, but I do trust them not to kill me in my sleep -- which is what trust is about (IMHO).
In fact I think I trust them more than I love them, and I love them a lot. But sometimes I'm upset with them. Being upset or angry doesn't affect trust.
Trust is a kind of binary quality that is either on or off; it may be too strong to say that love == trust, but I really can't imagine how I could love someone without trusting them.