My daughters names and family name

Molly is a diminutive of the name Mary, so I've used Mary below (I don't think Irish has a version of Molly):

Eimíle Nic Mhathúna [older form: Eimíle Nic Mhathghamhna]

Máire Nic Mhathúna [older form: Máire Nic Mhathghamhna]

I've enlarged the font for the names, so that you can see the accents clearly.

In case you are wondering, whereas the surname (family name) would be Mac Mathúna for a son, the Mac changes for a daughter to Nic (a contraction of the Irish for "daughter of the son of" ..."). and an "h" is added to Mathúna after the "m", for grammatical/pronunciation reasons.

For you yourself, a woman who marries may choose to keep her own surname or to take her husband's surname. If you want to use your husband's name, the Mac is replaced by Bean Mhic ("wife of the son of"), so your surname would then be Bean Mhic Mhathúna.

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.