If you have the Grand Hyatt booked and have the other boxes checked (transiting to a third country, etc), you will likely be granted a transit visa upon arrival. There is a counter for that. Like anywhere, however, admittance into the country is ultimately up to the immigration officer but a Mexican passport should not be an issue (ie not from Iraq, Syria, Yemen...)

To make things smoother/easier, you can book an arrival service (marhabaservices.com) who you can escort you through the process.

I you'd rather have the visa pre-arranged, see what the Grand Hyatt can do in the meantime. Tons of people have their visas arranged by organizations other than Emirates or Etihad.