My wife has a tattoo and I love it. So I'm a fan.
But please, please, please seriously consider some of the warnings posted here. First, there are health risks, not the least of which is hepatitis. I've been to Mexico frequently enough over the years to understand that the country's health and sanitation regulations, which on paper may compare to those in the US, are very often not enforced. The tattoo parlor you're looking at may be as clean as any in the states, but the way things work in Mexico, I have to say there's no way to be sure. And this isn't about getting a nasty case of Montezuma's Revenge, which is unpleasant but temporary. You can die from things that live on a dirty needle.
Secondly, there are the issues of having to keep it covered, out of saltwater, etc. Those are detailed in the posts above. Those restrictions can make getting a tattoo while on a cruise awfully inconvenient. Oh, and they hurt. Your skin is raw for the first few days. So depending on where you get it, you may have trouble sitting or lying down in certain positions. Do you really want to deal with all that on a pricey cruise vacation?
I think it's cool that you and your aunt want to get matching tattoos. But any talented tattoo artist in the US is capable of drawing a Mayan design. Just show them a design you like. They'll tattoo it on ya.
Perhaps you two can scope out a US-based parlor that you can visit immediately after the cruise, and then get those matching tattoos as a permanent reminder of your vacation. Get references and check the local BBB and Health Department for complaints. This business will inject ink deep into your skin by piercing you thousands of times with a needle. It's worth the effort to check the place out.
Have fun, and good luck with the tattoos - wherever you get them!