OP - if only your wife is on the mortgage, I can't see how she could claim TRS for both of you. As always, contact the TRS people in Revenue for the definitive view, but that's my opinion.
"Married" TRS doesn't exist per se: where two (or indeed more) people hold a mortgage on a property, and assuming all are owner occupiers and contributing equally, then the allowable TRS is the total of each individual's allowance, that is relief on up to €8,000 mortgage / borrowing interest at the standard rate of tax per person, or the total mortgage / borrowing interest, whichever is the lesser.
Kyla: Yes, it's January to December. You'll have to declare the income [form 11, I think], but providing you don't exceed the threshold - €7,620 income - you'll have no liability in respect of it. Do be cautious though: income of €7,621 and you'll be liable for income tax at your marginal rate of tax on all of it, which would be a very expensive proposition. If you're running close to the maximum late in the year, you can avoid incurring the tax liability - not to mention making a nice gesture! - by giving a reduced Christmas rent, or something similar.
It won't affect the TRS.