Romans 12:18 says "If it is possible, as far as it depends on you, live at peace with everyone." There are times when it isn't possible to live at peace with everyone, but we need to teach our kids to make the effort.
Pray for the person. It's difficult to be angry or actively dislike someone you are praying for. Praying for someone who is making your life difficult creates feelings of compassion for them.
Pray for the situation. Ask God to help your child find the best way to deal with the situation. Ask Him to change any of your or your child's attitudes that are getting in the way of improving the situation.
Don't undermine the other adult's authority. If your child hears you complaining about their teacher or coach, then they will begin to question that person's authority over them. Whatever concerns you have about the relationship need to be dealt with outside the hearing of your child. Undermining the other person's authority gives your child the message that that person does not deserve his respect.
Listen to your child's concerns. Don't simply brush off your child's complaints. Help your child decide whether those complaints are valid and whether the solution relies on your child or the person in authority.
Change the things you can. If your child is clashing with her teacher on something small like where to put her name on the paper or how to line up in line, then it's your child who needs to change. On bigger issues, like a coach benching your child for no reason that he can see, help your child focus on the things that are within his control. He can't change the fact the coach benched him, but he can work harder in practice.
Let your child deal with the situation first. If your child is involved in a personality clash with a teacher or coach, offer strategies for dealing with the situation, but let your child have a stab at improving the situation first. This gives them some control over the situation and lets them practice dealing with conflict. Be there to back your child up, but give your child the first try.
Come up with a plan for dealing with the situation. We often can't change the other person, but we can work around them. If your daughter is concerned about how her coach's practice strategies are affecting her game, see if you can find another practice for her to attend along with her regular team's practice.