The first is an English word. The second isn't - though you might see lovin' in songs, etc. Note the apostrophe, which means the end has been left off.
Similar answers apply to goin', comin', havin', etc. Know about it, but don't do it.
I'm afraid that is nonsense about RP. When I was growing up, many people thought that omitting the final "g" from any word ending "-ing" was an indicator of a lack of education or even of stupidity. Some people still think that but I don't think the opinion is quite so prevalent. Having said that, at job interviews and at formal occasions, I always recommend pronouncing all words in full.
'Untin', shootin' and fishin' were once posh pronunciations, but a very long time ago, when the upper classes didn't care about the niceties of language, which they, apparently, left to the middle classes.