I don't know if they are related Jim. I've not come across a Philip McGuigan or Margaret Fitzpatrick. You say that Rose Ann McGuigan was bnorn in Lanark in 1863. Do you know what parish in Lanark? Did Philip, Margaret and Rose Ann all emigrate to America?
I know my Rose Ann and you're Rose Ann are not the one and the same as my Rose Ann became a McGuigan through marriage but Philip could be a relation to John. Perhaps a brother but more likely to be a nephew or other relation. If you can tell me as much as you know about Rose Ann the next time I'm at the Scottish Records Office I'll find out what I can for you. Any other Mcguigan's you wish to know about let me know and when i'm there I'll carry out a search for you.