Hello Ellen,
Sorry to take so long to get back to you. I tend to concentate on genealogy more in the winter months. I am in Canada, trying to put the pieces together from afar as you are. Unfortunately my Connors did not stay in Tralee. They chose to move on to Killarney where they remained. I don't know that any of them immigrated prior to the 1840's and when they did they went to Britain. I have only traced my immediate lineage so I am not aware of the movements of siblings.
My suggestion to you would be to try to determine which ship she emigrated on and go from there.
Because there are so many individuals with the same forenames-John and Mary being Catholic in origin are the most common. So it's far to easy to get the wrong ones when you don't have concrete information.
The ship's log hopefully will give you the necessary clues to get to your next step.
You might wish to delve into the history of the the O'Sullivan Clan. There were two major Septs the O'Sullivan Beare and the O'Sullivan Mor. At some point you will need to ascertain which one you descend from. But that's a long way off. If you enjoy history you can get so many clures that help fill in the blanks when searching your kin. There are many O'Sulivan websites (just google them) that you may wish to join. They can be a great source of info-if not which families you don't belong to can be ruled out! I have been there!
How lucky you are to visit Tralee itself! It's a beatiful area.
(My great x4 grandad Daniel Connor left Killarnney to work in Tralee at the Ballymullen Barracks as their boot and shoe maker in the early 1840's.)
I hope your search is fruitful and that you have a lovely time.
Perhaps when you know a wee bit more we can compare notes.
Best of luck Ellen!
Best regards,
Nathalie C.