Pedroboy,
I cannot speak with any authority as I am just a member of BALPA. However, I think these injunction cases are dealt with pretty swiftly, so if the judge decides on Monday 10th to permit a strike, BALPA would probably give the requisite 7 days' notice shortly thereafter. So a strike could begin on the 17th at the earliest, which would probably curtail your family's visit I'm afraid. If they are able to change their plans now, I should think that would be a good idea. Alternatively, hang onto the tickets and travel at a later date.