Volunteer Coach for a 501c3 organization

You can deduct expenses you pay when providing service to a charity, including mileage, and sometimes meals and lodging.

You have put your finger on the problem.  You can deduct charity travel "only if there is no significant element of personal pleasure, recreation, or vacation in the travel." And "The deduction for travel expenses won't be
denied simply because you enjoy providing services to the qualified organization. Even if you enjoy the trip, you can take a charitable contribution deduction for your travel expenses if you are on duty in a genuine and substantial sense throughout the trip. However, if you have only nominal duties, or if for significant parts of the trip you don't have any duties, you can't deduct your travel expenses."

https://www.irs.gov/pub/irs-pdf/p526.pdf

I'm not aware of any specific guidance on your situation.  If you would be traveling anyway, because your sons are on the team, is it deductible, even if you coach the team or coach another team on the same trip?  

I think you have to look at whether you are "on duty in a genuine and substantial sense throughout the trip". 

It's hard to say more because the IRS is not more specific.

I will say that personally, I used to sing in the church choir, and I was the treasurer.  I deducted mileage for business meetings and extra trips related to being the treasurer, but not mileage to choir rehearsals and performances, because that felt more personal than business.  But that was just my view at the time.