Here's Michael's marriage to Catherine Casey:
Ireland, Civil Registration Marriages Index, 1845-1958
Name: Michael Clarke
Date of Registration: Jan-Feb-Mar 1885
Registration district: Celbridge
Volume: 2
Page Number: 481
FHL Film Number: 101255
(same details for Catherine, so a likely match)

Have you seen the 1901 census for Peter Clarke + 2 younger brothers, living with their grandparents PETER & ANN CLARKE in Celbridge town?

In 1911, Peter's brother MICHAEL is living with his uncle THOMAS CLARKE & wife KATE in Leixlip.

Perhaps Michael & Catherine/Kate had died pre 1901?

Good luck.