You're quite correct to say that many native English speakers cannot use the apostrophe correctly with 'it'.
There are 2 uses of the apostrophe - to indicate possession and for contraction.
Contraction is fairly straightforward, where the apostrophe indicates the missing letter(s), but possession does cause a few problems. 'It's' is always a contraction.
I think the problem with 'its' for possession is caused by the confusion between speaking and writing - when speaking, 'it is' is nearly always pronounced 'it's'. It would be much clearer if the two words were spoken individually. Take the following - 'The dog has a kennel. That's its home'. If there was an apostrophe, it would read 'That's it is home' in its (possession again) full form.
As for apostrophe and 's', I always taught that you only used this when the additional 's' was pronounced. For example, 'girls' school' would sound very strange as 'girlses school'. However, I would use apostrophe and 's' with 'Ross's house' because you pronounce the additional 's'.
But - and there's always a but - it is often a matter of individual preference. As long as your intention is clear, just find a method that makes sense to you and is easy to use and you should be fine.
Hope this is of some help.