"What are my chances?" is unfortunately not a question we can really answer here. There are two reasons for this.
First, we don't know enough about the case. All we know is what you've written here - which isn't much detail - and presumably, the other person involved would give a very different version of events than you would. A judge hearing a case hears both sides, and tries to give equal weight to both. The less information one has about a case, the harder it is to predict what will happen - and all we know here is what you've written.
Second - single-event probabilities are arguably logically meaningless. Consider this: Suppose I said you have a 75% chance of winning the case. Would you feel reassured? And, suppose I said that, and you lost. Would I have been wrong? Probabilities are meaningful only when you are considering a lot of similar events - but legal cases are all so different that it's hard to draw valid comparisons.
To best increase your chances in a court case, you should consult in private with an attorney in your area. I realize that isn't the most helpful advice, but I do believe it's the best.
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I agree with my colleague that it is hard to provide you with an answer as to probabilities. Practically speaking, living 40 miles away may make exercising the right of refusal provision more difficult but not impossible. Think about incorporating notice provisions as to when the custodial parent would have to notify the noncustodial parent and how long that noncustodial parent has to respond and accept the parenting time. Making all provisions mutual is helpful as well.
Just some ideas...if the Mothers argument is that you lve too far, you couLd ask for larger chunks of parenting time like longer weekends and midweek overnight to cut down on the back and forth travel.
If the Mother raises the DUI and unsafe driving, you could agree to a provision that neither of you would drink or use illegal substances while the child is in your care.
Good luck at your mediation! I wish you the best!