Thanks to you all for research and good ideas. I will try to respond with what I have got so far and to your queries.
Services from Fleetwood (on England's Lancashire coast) to Belfast and Derry started running on an occasional basis in the early 19th century. A scheduled service started in 1843 so I think that John Whiteside and his family used this instead of the Liverpool service as Fleetwood is very near Samlesbury.
John my 4 x great grandfather appears in Lancashire before 1798, whether he was born in Ireland or not, when he would have been age 21, when he was recorded as marrying Jane Salthouse, who I think was his first wife, on 9th December 1798. The dates and times fit, plus the fact that St Chads in Poulton le Fylde was also where he married his second wife ten years later and where Richard and Agnes were baptised in 1818. Evidence Lancashire Parish Records Online. They lived there until after Jane died at Highfalong and John was a Husbandman. There were sons: Henry, John, Robert Samuel before Jane dies in 1807. One later died in 1808.
John Whiteside then married Betty Rimmer by Banns legally published by: Thos. Turner Vicar of Poulton on 16th November 1808 at St Chad's, Poulton Le Fylde, Lancashire. He was a widower and she a spinster both living in Marton, Poulton le Fylde. St Chad's features in all these records. John probably needed another wife to look after the remaining three sons.
There is a gap in births in Lancashire Parish Records Online for John and Betty from 1808, which would fit the Militia Theory but on 23rd September 1812 Jenny Whiteside was born at Carleton and baptised on 25th October 1812 at St Chad's, Poulton-le-Fylde, Lancashire, England, which is where John Whiteside married Betty Rimmer four years before. Jenny Whiteside is said to be the natural daughter of Betty Whiteside but John her presumed father is not mentioned. Maybe he was away.
Richard, my ancestor was born in Ireland in 1815 and Agnes in Cockerham in Lancashire in 1818 when they were both christened and John is now said to be a cordwainer, shoemaker. If John was in the militia maybe he learnt the trade there. The theory is that Richard and John and probably Jenny all went over to Ireland to be together.
How do I find out if Richard was in the miltia which maybe would explain why Richard was born in Ireland? Does this also mean he had dual nationality?
NB St Chad's Church is C of E. St Michael's Church in Cockerham is Anglican so this suggests that the Whiteside's were C of E.