Mommsen will captain the side following the injury which saw him miss last week's matches with New Zealand A. He is joined by Nottinghamshire wicketkeeper Cross, who has reclaimed the gloves from Northamptonshire counterpart David Murphy.
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However, county commitments have again ruled out regular captain Kyle Coetzer and left-arm seamer Rob Taylor while pace pair Ruaidhri Smith and Gavin Main are injured.
Scotland coach Grant Bradburn said: "I've been made aware there is an intense rivalry and that is something to relish.
"But the main thing is that the players take the opportunity to enhance their chances of making it onto the plane to the 2015 World Cup."
Scotland squad: P Mommsen (c), M Cross, H Gardiner, C MacLeod, M Machan, R Berrington, J Davey, M Leask, M Haq, A Evans, I Wardlaw, F Coleman, S Sharif.
Ireland: K O'Brien (c), J Anderson, A Balbirnie, G Dockrell, J Mooney, A McBrine, G McCarter, A Poynter, S Poynter, M Sorensen, S Thompson, A White, C Young.