For starters, you need to get a good feel for your new player's skill level. Once you know that, then it is time to build up her confidence.
At PCA, our Double-Goal Coach training contains a section about the ELM tree of Mastery (where ELM stands for Effort, Learning, and Mistakes are ok). When you tie ELM into this player's performance, it will help her understand how -- and why -- to continue expending maximum effort through those tough competitive situations.
Intentionally exposing her to safe, legal, physical play in practice will help her get used to those situations. It also will help you assess the validity of her father's concerns. Either way you, as a coach, will have a basis from which to operate, both in terms of improving her play and in equipping you to discuss her progress with her father. Creating these tough-play scenarios also will help the rest of your team learn how to respond.
Concerning your player's father, PCA teaches Second-Goal Parents� to offer their children unconditional support, regardless of athletic performance and game results. Given that your player's father already has threatened to remove his daughter from your team, your player likely is "looking over her shoulder," and her performance may be suffering from her father's pressure.
No matter what you do for her on the field, her father's unconditional support is vital to her as a person and as a player. Hopefully, you can bring that about by some combination of elevating your player's game and encouraging her to discuss her feelings with her father.
You also should approach the father, privately, and start a discussion assessing his daughter's progress. Perhaps he will have noticed improvement and can lighten up; or perhaps you can explain the steps you are taking and get a feel for whether he is more pleased with his daughter's performance.
You should ask him to help fill his daughter's emotional tank by offering truthful, specific praise that positively reinforces her improvements, rather than draining her tank by threatening her. You also can suggest he read Positive Sports Parenting by PCA Founder Jim Thompson.
This conversation should come across not as your telling him how to parent, but what steps you all can take to bring about the shared desire for your player to perform at the highest level possible. And, if you can honestly say how hard his daughter is trying, how much she is improving and what a terrific all-around person she is, perhaps he will get the message that he should be more supportive and less critical of his daughter.
(A member of the Long Island Lacrosse Hall of Fame, PCA Trainer Lisa Christiansen has coached at multiple levels, including serving as a team manager for three world championship U-19 US National Lacrosse teams.)