I'm pretty sure I will need to put the xbee's in API mode since there will be three
That would depend on whether you need one way communication or two way, and how responsive the communication needs to be.
In AT mode, the sender could broadcast a message that all units would receive at (nearly) the same time. The actual sending of the message might be delayed, until it was clear that no messages are being sent.
So im thinking that the arduinos at the dataloggers should transmit and receive between each other for the periodic signal and they both should receive from the handheld unit for the intermittent pulse.
Why do the loggers need to talk to each other? If they are going to, what is the third unit bringing to the party? One logger could simply send the signal when it is time for both loggers to do something. Whatever that something is.
3 xbee pro XSC's (for maximum range),
Up to 15 mile units to transmit 300 feet? OK.
Let me know if you see any major flaws in this idea or improvements without making it too complicated.
You haven't said what the idea is, other than to send "signals" from something you don't have yet to something else you don't have yet.
Also, could you direct me to a project that has some simple commands like this sent wirelessly?
"Simple commands" and a single pulse are two different things. While you are buying stuff, though, Rob Faludi's book "Building Wireless Sensor Networks" would be a good investment.