Hi Searching, there is no record to suit on Roots Ireland of your children or any children to a Hugh Malone and Bridget Mahon, there are children to a Hugh Malone and Bridget Farrell but the 3 are much earlier and only Francis born in 1849 is on the names you give. Farrell is a common name in the area.
On the plus side I found the marriage of Anne to James MIley in 1906, she is full age and her father Hugh is deceased, was a shoe maker, you can view the certificate for free here https://www.irishgenealogy.ie/en/ click on Civil records and enter the name and year and then sign in, there is no fee, the church records are not there for the area and civil records for all BMDs commence in 1864, however the only Hugh death I see is in Carrick on Shannon (in Leitrim and near Longford) he is 66 in 1873 I think, no other info to take us further other than this man was a labourer, he was also a widower. https://www.irishgenealogy.ie/en/
I cannnot make out the address given on the marraige cert but Roots says he is from Lisduff and she is from Longford, Longford is a county; a town and a parish. Unless Hugh was know as Hugh but used his own name for official use, ie if he was Patrick Hugh he may be known as Hugh to separate him from the other Patrick's in the family.
Otherwise there are two private Facebook pages on Longford genealogy, one of that name and the other a DNA page, I have assumed they were Catholics in case they did not register the births post 1864, this would carry a possible fine so usually done, Church of Irleand records may have been lost in our civil war as about 40% were lost, you can visit there Irish site for a list of available records.