If she left it on the floor, it would have been easy enough for him to catch it with his foot thus kicking it. In fact, I did that to DH's.
But it didn't break.
However - the problem you describe - and I could be quite wrong but I had that happen to my previous laptop. I thought it was a connection problem between screen and rest of unit but it turned out to be a fundamental motherboard problem that ended up with me needing a new laptop.
Therefore, its really a tricky one because if it is something unrelated, which is possible, you could end up essentially buying your mum a new laptop for something which was nothing to do with DS which seems unfair.
I actually am of the opinion that if someone knows they are having a child around beforehand (so you didn't just "drop in" type thing) they should move things like this, depending a bit on age etc. Fine if they are on a table and the child is 4 but not fine on the floor as its a bad place to keep such things. Always depends on context etc.
If its a small repair though I would pay to avoid bad blood but beg request that she leave things like this out the way next time.
I'm going to my in-laws for Christmas. There will be lots of kids around, including my own. Some will be too young to really understand how delicate a laptop is. But if I leave it somewhere and one of the kids break it, I wouldn't dream of asking the parent of that child to replace it - particularly if they were not even there. So in a way I think your mum is out of order but depending on the circumstances I might pay anyway.