there is no point in contacting the vicar, same considerations apply to grave plots prior to late 19th Century - Michael yard is better preserved than Old Ballaugh but again you need an MI to locate the grave.
These burials date early 18th century - it would appear from what records survive that your presumed ancestors were tenants of the Bishop in the Bishop's demense which straddles the Michael/Ballaugh border (see page on manxnotebook) - an infant burial would not I suspect be accorded the same consideration as that of an adult member of the family in that the infant might well be buried in an area away from the main family plot if that was not suitable (eg had had a recent burial) - MI's were not that common before early to mid 18th Century - many grave markers were I suspect were wooden crosses or boards which soon rot, with a flat stone laid over the grave to prevent disturbance by dogs - some of the older surviving Michael markers now vertical would appear to have been originally flat on the ground