I'm confused by the 12 year old still in primary? Even if you deferred, they'd surely be off to secondary this year? Unless you're in an area that still has a lower, middle and upper school system and you actually mean they're at middle school? Although I thought lower school went up to Year 4 and therefore the 7 year old wouldn't be going to middle school yet? I'm not sure of a system where all 3 could be at the same school unless it's an all-through, which I can't imagine in a rural setting.
I think I would consider moving them, yes. Even if you get on with SIL, that's a bit too close for comfort. Children need their own space at school. It must be stifling enough for them being at such a small school that they have their siblings in the same class, let alone the teacher being a relative too.
Did SIL check with you how you felt before applying for a job there? As a teacher myself, I couldn't imagine going for a job somewhere so small that I would definitely end up teaching a relative or close friend's child, without checking first how they all felt about that. She's completely changing the dynamics of their school life, and that's not fair.
I wouldn't move them to your school though. An hour away is madness. They'll be exhausted from the commute, have no local friends and will still have their mum at their school even if you don't actually end up teaching any of them. I'd look for other local options instead.
It doesn't need to cause problems with SIL. Just explain that you feel it's only fair the children have their own space away from family at school (this would be much harder to justify if you move them to your own school).