I have been told that a Catholic family would have baptised a child at the nearest Anglican church - is this correct?
If they were strict and devout Catholics then I think that's extremely unlikely. The Roman Catholic church does not accept the validity of Anglican orders (ie does not accept that Church of England ministers are properly ordained), and is always keen for the children of its members to be brought up under its own influence - often in a very exclusive way.
C of E teaching is that in an emergency, baptism can be administered by anyone at all (eg a midwife); I think this may be RC teaching too (but I'm not sure), in which case they would (grudgingly?) accept an emergency baptism performed by a C of E minister as being better than none at all. However, in normal circumstances I think the stricter teaching would apply.
On the other hand... not all Catholics stick rigidly to the letter of the law at all times, and particularly if one parent was a non-Catholic, you might need to consider the possibility of a baptism elsewhere.
In a nutshell, never say never, but I think there are more likely possibilities.
Arthur