As this ELU answer indicates, the correct version of this phrasal verb is actually to home in (to head directly towards a target). But OP shouldn't let that bother him; quite possibly most native speakers use the "wrong" version.
So the combination isn't really in + on - it's home in + on. It occurs with other phrasal verbs of the general type [verb] in, such as...
I'll look in on you this afternoon (to look in = visit briefly)
We'll check in in the afternoon (to check in = confirm arrival - at a hotel, for instance)
The burglar broke in in the night (to break in = enter illegally by breaking a lock or window, etc.)
As those last two examples show, although it might look a little odd to some, there's nothing "incorrect" about repeating even the same preposition. The first occurence is part of the phrasal verb, the second is just a normal preposition indicating the relationship between verb and object.
EDIT: Per comments below, I've just changed "sound a little odd" to "look a little odd" in the above text. The stress patterns of normal speech mean you'd barely notice the same preposition occurring twice (one would normally stressed, the other not, so they'd sound very different). But in the written form it's distracting/off-putting for the reader. Suppose, as per @J.R.'s example, your first thought was to write...
I didn't understand what she was getting at at first.
In that particular case, you could just insert a comma between the two at's to help the reader along, but it's only a partial solution which won't always work. Unless you're committed to accurately reporting actual speech, a little rewording is probably better...
At first I didn't understand what she was getting at.
Because he didn't stand up: he didn't rise from (out of) his seat, he raised his body a little bit while still in his seat. He "moved from a lower position to a higher one" while still in his seat.
rise
1 Move from a lower position to a higher one
(Oxford)
To be 'in' his seat means to be 'enclosed' within his seat; so one can rise in one's seat by raising or boosting oneself up by several means. One's bottomside does not have to be in contact with the seat bottom to be considered in one's seat. Etiquette might say that, but grammar doesn't
I believe the difference between onto/on to and/or into/in to has been covered previously; search for it and if you can't find an answer, ask a new question.
Best Answer
It's incorrect to use have in the first sentence, since the subject ("Christmas card") is singular regardless of the adjunctive phrase ("along with the letter").
Along with and together with are interchangeable, and to my ear, neither implies whether they should be in separate envelopes.
Even if there is some indication one way or the other, it's best not to leave specific instructions up to implication. If you have to ask about it, chances are very good that it will go over your sister's head.
But as you addressed all these concerns at the end of the question, I feel I hardly need to interfere: