Mrs Rosa - maybe I tend to be too brief however
(a) there is only one set of twins - the father was named in the register - the mother was NOT - there is nothing unusual about this, the woman of a married couple was not named at this period in Ballaugh records. In fact the only women named were those producing illegitimate offspring (or very unusually women of 'higher' social rank). Thus in the register there is no mention of an Alice Corlett - any supposed records you see are a figment of some 20th century mormon's imagination based on guess work. In the Michael register the custom was somewhat different in that the woman's christian name was generally given and sometimes her family name. In both registers the parish clerk often added notes as to the residence of the parents - these notes are totally missing from the IGI yet are often vital in determining parentage. Parishes were not divided by a 'Berlin' wall but people living near the boundaries might use either church though they might have a family burial plot in one as well as a part of a pew allocated to them - it was this migration of nominally parishioners of Ballaugh to the much nearer Michael church that is reflected in the command issued by Bishop Wilson that they should use Ballaugh in the future.
. But if you have to carry a young baby for baptism in winter or poor weather then going to the nearer church is very attractive - usually in such cases the parish of the 'visitors' is noted - or as in Michael + Ballaugh Bishops land/demense.

Now to return to half bothers + sisters - presumeably the only problems were by shared fathers as maternal half siblings would generally know each other. If you look at the various ordinances then it was a church command that midwives find out from the woman during labour the name of the father - in those days most illegitimacy was the result of a failed courtship and the woman would know the father (women of ill repute would also be known very quickly). Sometimes this information was known to the vicar at the time of baptism othertimes it would comeout during the court case following the birth - if the woman did not give the father's name then she could claim no allowance towards the cost of raising her child
I hope this explains things - it is pointless to apply today's standards or expectations to a distant period.