If you travel tomorrow (after a 29 hour delay), Direct Line will pay you £30 per person under Section J (Part One) of their policy, which states that the delay is calculated "from the time shown in your travel itinerary".
You also have the option, under Section F (5), to abandon your travel plans. Direct Line should then pay for "for your personal accommodation and transport charges that you cannot get back from any other source" (less an excess of £40 per person). However there seems to be no cover for such things as cattery fees.
Source:
http://www.directline...leTravelPolicyDoc.pdf
Chris