I think that whoever is in charge in London will be desperate to maintain control of Ireland, regardless of the status of the Scots; nobody in the period had any desire to get out. Although Ireland was a resource sink, it wasn't seen that way; it was seen more as a land ripe for colonisation and improvement. There was also the strategic issue; if England doesn't exert control over Ireland, somebody would- and ITTL, that somebody now includes the Scots, who have major interests in Ulster and could potentially be a threat.
Given these circumstances, a Commonwealth of England and Ireland, or something similar but a little more semi-detached, seems overwhelmingly likely, unless something dramatic happens.
Such as?FILLER