Hi Karen,
I will see if can I help you. First of all Clarkes in Cavan as you may have guessed are very plentiful as are Reilly's. My grandmother was Clarke and both her parents were Clarkes, therefore I have nine John Clarkes, four of them born around 1870 and some did go to America.
The best course of action is to go back one step at a time. If you look at your fathers records, who are his parents? You should find this on his birth or marriage records and then follow up on the records of his parents likewise including their birth, marriage, death and burial records. Did they get married in America? Who did he come with? Where is he listed on the census records, who is he living with? Did he ever complete draft records for WW1 or WW2, these often state a next of kin etc. Using that information you hopefully will build up a wider family. Very often there is chain migration which means that they may have brought over younger siblings, if you can find the most recent of these, the shipping records might have the name of the townland that they came from and more importantly the name of the person that they knew from whence they came. Look for their burial records and at their headstones, I have seen headstones with their townlands on them, you may get lucky..
The parish and townland is what you need to help you eliminate the wrong lines. The Irish Government has set up the following website and you can use this to search for your ancestor https://www.irishgenealogy.ie/en/ it is free to search and if some of the images are not available to view, they can be purchased. Roots Ireland is another site, it is a subscription site and covers the church records, the originals are available for free at https://registers.nli.ie, but you need good eyesight & tune yourself into the handwriting. The name John Clarke is common to all religions, so if you can find out what religion he was, you will also be able to eliminate non family. As you are tracking John Clarke you can use http://www.census.nationalarchives.ie the 1901 & 1911, if the John Clarke is still listed in those census records, he obviously is not yours.
Try and look at the original documents as transcribers may indeed pick up Kelly as Reilly and visa versa, many sites will allow amendments but it may take them some time to make the changes. Take note of the names of the children, see can you find the naming patterns ie someone was named after his father or her father etc. So when you look at the names you have listed are any of them repeated? You state that Francesca has two surnames, it may suggest that this is her second marriage so follow that up and find out when did she marry Thomas Clarke, Redfern or Rattison is not coming up in Co. Cavan, there are some Pattersons. People in Ireland around the time your John Clarke was born often married their neighbours, though not strictly so if they travelled for work.
Pull out all the old photos, look at the back of them, chat to all your family and any neighbours, someone may have a story you may not have heard, neighbours will have the stories your family will not tell!!
Good luck with John Clarke, if you can identify a townland, do let me know, I may be able to then help you further or he may even be one of mine.
Regards Carmel