Is the timeline like this:
? Drops kids at school. Leaves car there.
Walks to river towpath - seen by someone at 9:15
10:15 someone finds the loose dog and takes it to the school (maybe recognised the dog / knew the owner or her route).
School rings her partner to say ‘we have your dog’ partner calls police (before going to collect dog / look for partner) and police turn up at 10:30am to search for her?
Is it usual for police to respond like that - I thought someone had to be missing 24hrs before they would consider them missing - because she could have just been further along looking for her dog?
Is it likely she had a MH vulnerability that alarmed the partner and the immediate police response was a welfare check?