Dear Butterfly,
As my former French Teacher would say "what you don't know 'bout, leave it out." he was referring to exams, but i found it works in life, at work, in general.
Some people do enjoy being asked about their comings and goings. Especially in this case if she is new to the US as I understand it? I however grew up kind of left and right and found questions about where i'd been tiresome... they always came from people i did not know well and with whom i did not wish to share. you could ask how she is doing after the move, focusing more on the here and now... has the settling in been smooth for her in the US? stay general... give her a chance to 1) share OR 2) give you a short vague answer and change subjects.
Personally, i'd much rather be asked more "superficial" and common things at first, and i do the same. have you seen <recent movie> ... did you like it? do you read much... enjoy music? gardening is one possibility, or the more general "how do you like to spend your leisure time?" i also like the other person to share if they are going to ask a particular question. so if asking specific questions, best to ask about things you are interested in. don't ask if she collects stamps if you could care less to have a conversation about stamps!
you and this woman have at least one really "easy" topic in common too... your kids... you can talk about how they were as babies, when they started to talk, were they fussy or quiet, etc... talk about your experiences as moms.... you probably had very different experiences with each of your kids.
also, nothing says you have to "lead" the conversation. you can let her lead. if she misses South Africa, she might start talking to you about it without being asked. that might be entertaining. if so, then you can ask questions in the context of what she tells.
it can also be nice to sip tea and relax in company, yet not maintain rigorous conversation. just sit quietly at times, perhaps with the odd comment. that depends on the company - some can do it, some can't. i rather like it.
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i chuckled at the Queen of England question, because i've been asked that before. i doubt you came off as duhhh. trust me from personal experience A LOT of folks are not aware of when (or sometimes WHETHER) former colonies, gained independence, unless they have lived there personally. I don't! so, i wouldn't worry about seeming DUHHH. And although I may not have liked to be interrogated on my comings and goings, I never thought anyone stupid for their curiosity, or even misconceptions. You personally strike me as a bright individual... i'm certain that comes through in person. Remember that even the most intelligent people don't know everything about everything! So lay your worries to rest, in that department.
Mostly try to relax and enjoy yourself. Go with the flow. ~~~
~ waves ~