The RIC Index compiled by Jim Herlihy contains 38 Glennon names(including variants). There is only one Robert born 1840 a brother of your Joseph. Their Father(Robert) was not in the RIC but two of their brothers William and Thomas were.
Joseph Glennon Service record 39642, height 6ft and half inch, joined the Sevice 7th August 1873 age 19. He was located in Wexford and resigned from the Force 23 June 1880 due to injury
Joseph married Mary Anne Hanlon in Enniscorthy Co Wexford. The marriage was not registered with the GRO but I recollect seeing that it was recorded in an index of Enniscorthy Church records. i will make a search thro. my papers
You will see from the birth search on site that the couple had three children Mary Agnes 1877 Robert 1880 and Matthew 1882
Robert Glennon ( Joseph's brother) married Catherine Duffy mid 1860's and had possibly ten children. He died after his retirement from the force and Catherine moved to the US with the children. Another of Joseph's brothers is believed to have emigrated to Australia(possibly Christopher ?) William who was also in the force died 26 October 1882. He was married to a woman from Mayo on the 9th September 1877-I have not searched any further details