If I’m trying to relocate 61 miles outside my current parish and my ex is fighting it, what are my chances of winning in court?

I assume that there is a custody order currently in place. If so, a court must grant permission. A move without such permission measn that you are in contempt of a court and could be charged with parental kidnapping. The burden will be on you to prove that a relocation is in the "best interests" of your child. Each petition will be reviewed by the court on a case-by-case analysis. There are numerous factors the court must consider in determining whether removal is appropriate. They include, but are not limited, to:

• Why the relocating parent wants to move;
• The motivation of the parent opposing the move;
• The advantages of relocation in terms to improve the life of the child;
• Any disadvantages of relocation on the minor child;
• The likelihood that a reasonable visitation schedule can be arranged with the non-custodial parent;
• A chance to bond with extended family members.
• The likelihood that the parent desiring the move will comply with visitation orders after the relocation. 

You should be aware that a parent who wishes to relocate because of a job, new spouse or to care for sick relatives will have a stronger case than a parent who simply wants to move away from the non-custodial parent. Additionally, the closer the relocation to the current location the better. In your case, for example, a 61 mile move will be looked at more favorably than a long-distance relocation.