It sounds fine to me. (But I'm not actually a native speaker, and Indian English does have a reputation for using the progressive a lot.)
This is how I interpret "I'm loving it". (I've put back the 'g' because writing lovin' is too folksy for me.) I also assume "it" refers to something particular, like McDonald's or the food there. Also, I think it helps to consider the analogous sentence "I'm enjoying it".
English certainly uses stative: I love chocolate, or I enjoy classical music. This expresses your position on something. But suppose I'm at a play/concert/movie, and someone asks me what I feel, during the event. I may say "I'm enjoying it" or "I'm loving it (at this moment / so far)". This seems perfectly natural to me, though perhaps not to native speakers everywhere.
There's also a difference between "I love it" and "I'm loving it". If you love chocolate, it only says what you feel when the issue of chocolate comes up, but if you are loving McDonald's, it implies that you're there right now and/or are actively engaged in thinking about it and loving it. (Just as "I'm enjoying classical music [right now]" means more than "I enjoy classical music".) Presumably, "I'm loving it" is a subtle suggestion that you too, like the speaker of the slogan, ought to be at McDonald's right now and actually get on with the act of loving it, not merely think of it as a nice place to visit from time to time. :-)
"According to so-and-so" is a well-accepted phrase to indicate a certain level of authority. It doesn't mean authority in the sense of indisputable, world-class, absolute authority. It means authority only at the level of indicating that this is the person to whom the statement can be attributed.
It therefore has rather wide usage, all the way from according to my brother, Nancy went to the dance with Frank, right on up to according to Einstein, the universe is curved.
The lowest level of its reference to authority, however, is the second person, according to you, which sometimes is used sarcastically, thus: According to you, I should never have bought stock in Microsoft. Boy, were you wrong.
We don't take it down to the first person, because that becomes overly emphatic, or to put it another way, redundant. According to me is simply saying, this is what I say. It isn't considered necessary to say this is what I say when you say something. You just say it, don't you? I can tell you Nancy went to the dance with Frank without saying According to me, Nancy went to the dance with Frank, you see?
If we look at your examples, Mari-Lou, we can see a little bit more of why the usage sounds a bit strange to native English speakers. Since we do imbue a bit of authority to the according to locution, we usually feel according to my brother, our father will go to a nursing home someday does sound odd; we would instead tend to say my brother thinks our father will go someday, and the response would be but I don't think so rather than according to me he won't. According to in standard English usage is given some weight of authority, even at the lowest level. It isn't taken as purely opinion.
Best Answer
Short answer: It sounds a little weird.
Long answer: As your research may have shown, "[poss. pronoun] + own" is grammatical English, as per this Oxford Dictionaries definition:
See especially the second example "the style had its own charm."
Adding in "own" can be used for emphasis. For example, imagine this dialogue:
It's one of those turns of phrase that's hard to think about. It just has to naturally slip in there. I have the impression it's more common in spoken English than in written English, but I have no data to support that claim.
About your question:
Personally, I feel "My own hometown" sounds a little bit redundant, because the relationship is implied in "hometown" already. I would remove it.
There's something to be said for the parallelism between the speaker's and their children's hometown. It's a choice of writing style at this point, but I would still stylistically remove it, but it wouldn't be wrong to keep it.
"Their own hometown" is better because it implies that their hometown is not the same as the first speaker's hometown. In fact, it's a very good turn of phrase to imply the speaker feels strongly about their hometown, but hopes that their children will develop similar feelings about the (different) town they're being raised in.
Yes, that's precisely what it says. I imagine the majority of readers would understand this sentence that way. If you wanted to imply it was the same hometown, you could say "... my children to love (it) too."