A bad day

I've been having a bad day recently.  Since about March, actually.

I work in a support role at my company.  I have teammates halfway around the world who also support many of the same people I do.

Recently, however, one of those teams we support has been in fire-fighting mode.  They're placing demands on my time as well as my colleagues off-site.

My off-site colleagues best know the system supporting this customer team.  I have an incomplete working understanding.

The system is located where I am.  So's the customer team.  So when then nighttime and network problems hamper my colleagues' efforts to keep the customer team happy, guess who gets stuck with the problem?

The thing is, I'm supposed to be working something that's also high-priority, but on another project.  So whom do I tell to kiss off?  Politely, of course.

Yes, I know, this sounds like a first-world problem to me too.