The answer(s) are (i) and (ii), but more of (i).
Studies have firmly established that language acquired during the language acquisition period below around ages 6 or 7, will be spoken without accent as respects the native tongue (wherever that might be), whereas, a foreign tongue acquired (or, as you put it, learned) after the ages of language acquisition will always be spoken with some measure of "foreign" accent in the adopted country. For example, a child who acquires both Mandarin Chinese and East London English, say, by the age of 6, will always speak "native" Chinese and "native" (dare I say it?) East-London-inflected English. You can take comfort also in the fact that you will never "lose" your own home accent even as, over time (with or without practice or mimicry), you come to make your pins and pens better understood. And your child will not "suffer" deprivation in any manner for your lack of facility with his (now developing) Mancunian accent.
By the weigh, is Mancunian a dialect that might tend to limit his opportunities one day? Will he be exposed to a standard dialect (educationally or otherwise) of a more UK universal sort? I would expect such a large city would produce speakers (and listeners) who could "fit in" anywhere, even among those speaking "Queens English." But I am not a Britisher other than by long, long-ago extraction (maybe just like you).
In this country people from some areas used to encounter career advancement problems, say for example, with Texas (or other Southern) accents--incidentally, if you wanted to hear perhaps the best modern version of Elizabethan (I) English, there was probably no better (or other) place to go than a certain enclave of Atlanta, Georgia--believe it or not; but I digress. (I grew up in the linguistic center of the U.S., so whatever accent I might have apart from standard, has travelled very well in this country.) With the spread of mass communications and the increased attainment of higher education in the populace, such problems of dialect handicap have largely evaporated...the U.S. is gradually blending into a single, national "accent." I would suppose something similar would be happening in England as well.
It is too bad...your encounter with Pen-less speakers; colloquialism and provincialism can certainly be a challenge, but one that grows more agreeable with time and patience. (For example, if Lord Baltimore could come back to life in Maryland, he would probably be appalled at what passes for English in, "Balmer Melan, his namesake city.)
All in all, the fact of your new neighbors' misunderstanding of a standard pronunciation should be an object lesson regarding an important truism of spoken language: that the principal "organ" of speech is not the mouth but, rather, it is the ear. So do not worry. Yours and your neighbors' "speaking" instruments will be in tune soon enough.