will a 700 x 35c tyre replace a 26 x 1.25 tyre

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No, a 700cc will be too large, the late Sheldon Brown does a great explanation of tyre sizing if you want to look further.
 

soulful dog

Veteran
Location
Glasgow
No 26 and 700 tyres are not interchangeable. The first number in the tyre size (i.e. 26 x 1.25 or 700 x 32) refers to the rim size of the wheel on the bike (the second number is the width of the tyre). Generally speaking mountain bikes have 26" wheels and road bikes (including cyclocross bikes) have 700c tyres, and one won't fit the other.

See CTC's tyre size table - the only tyres that are interchangable are some 28 and 700 sizes. I found this table a little easier to understand than the Sheldon Brown pages HLaB linked to, though I am to be fair, easily confused!

A possible replacement tyre for your daughters bike is the Schwalbe CX Pro?
 
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