Coming from an area with many facilities within a relatively small radius, I'll admit that I've never thought about your problem; but I can certainly see the problem that your community, and many others like it now face.
Obviously it's too late for this year, but maybe now is the time to begin laying the groundwork for next season. Would it be possible to have your organization included in the "larger community's" league or association? Obviously the preferred way would be to retain organizational autonomy and just be scheduled as any other team in that league's age group. Absent the league's willingness to do that, if your organization is willing, they could offer to just become a part of the other organization, which would obviously be less than ideal, but perhaps better than subjecting families to 2.5 hour drives every weekend.
In traditionally non-hockey markets like where I live in Texas, we do not have the small community rinks like northern states do, so all hockey is in larger cities which typically can field enough teams of each age group to play within their city. However, travel teams may not have enough competition within the smaller markets to make playing locally possible. The arrangement that is used is to have Dallas be the hub city, which manages the league. Travel teams that are members come from as far away as Tulsa, OK, and Houston, TX (both 4 hours from DFW, and 8 or more from each other). There are smaller cities included as well: Amarillo, Oklahoma City, San Antonio, Austin, Shreveport LA.
Anyway, this relationship allows teams to get the competition they need and want, without having to travel to tournaments every weekend. There are even cases where Tulsa or Oklahoma City would travel to Dallas to play the San Antonio, or Shreveport team, for example. I realize that I'm talking about "travel teams" here, and parents do sign up for the team knowing they'll have to travel, but within Dallas, there's enough competition that all of the organizations could get plenty of competition without having to drive more than an hour to play any of the local teams. Adding these other teams to the league provides benefit to all of them.
Hope this helps in some way. Best of luck!