Japanese Language/Usage of words without confusion
Well, I often do not dare to use kare/kanojo due to being afraid people mix them up with the boyfriend/girlfriend meaning. Are there any ways to differentiate them? Or is context the only way?
Also, which meaning does this sentence convey? "Kodomo ga iru toki,....". Does it mean, "when the kids are around" or "when you have kids"?
In general speech, merely the context determines which meaning you have in mind. There are obviously other ways of denoting significant others, but kare/kanojo remain the most used. And, if you think about it, if you have a significant other, it really doesn't matter in terms of denoting the subject to say "my girlfriend" or "her", since they refer to the same person.
Similarly, "kodomo ga iru toki" is also determined by context. If you don't have kids, you must obviously be talking about a future time or perhaps some other kids nearby that you were just talking about.
In writing, and to a lesser extent, you can qualify the conversation if it's confusing. Saying, for example, "Kodomo ga mawari ni iru toki.../when the kids are around..." or "Watashi wa kodomo ga umareta ato.../After i've had kids (lit., given birth)", but generally, you don't need to and these just sound "wordy".