What's the Name of That Book??? discussion

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Half Magic
SOLVED: Children's/YA
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SOLVED. YA - kids find magical quarter that can transport them to different times [s]
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Pretty much spoilers from here on, as it's describing various plot points as they arise:
It's a group of kids, I believe all are related as siblings. They find a quarter that can transport them places - if I remember correctly, just by touching it. The first place they get transported to - by mistake, as they think it's an ordinary coin - is a desert, where they have to deal with a very gruff man who threatens them (and I think was riding a camel). At some point, they end up visiting medieval times, with King Arthur and the Knights of the Round Table. I believe they also get up to some shenanigans in their own time, at one point breaking into a rich neighbor's drawing room.
One line of dialogue I specifically remember, was, when asked what time they come from, the oldest of the kids replied: "20th."
Also, I remember there being a bit of family "drama" in their current time; their mother was dating a new man, and they were understandably nervous about the situation. I think they visit a park or a garden at one point together as a family, and they all think it goes rather well - an "audition" of sorts for the new man. They're happy their mother is happy.
Any ideas?