I would put in both an urgent C100 for PSO at 48 hours notice (you can try for ex parte but it's more likely to be an urgent 2 day hearing). And at the same time put in a C79 form enforcement and mention in both applications about the other application.
If you want to try and get it ex parte then really you need to go into the court, first thing in the morning (9.30 maybe, depending what time the court opens - but as soon as it opens) with the application, and wait. You might get a same day hearing.
Otherwise, you can still take the application in (saves a day rather than posting it) - and tick for a 48 hour hearing in the section on the C100. It asks what you have done to notify the other party of the urgent short notice application and you can just put "will text when hearing date issued". As they expect you to put her on notice. But don't text until you have the court papers with the hearing date. That's the advantage of going into court and waiting - you can come out with the court papers in your hand for a date a couple of days later. The court might ask if you want them to serve the papers, so say yes - then it's up to them if she doesn't get them in time, but you'd still better text her with a screenshot of the court papers and just say something like "This is to inform you there is an urgent court hearing at x court on x date at x time which you're required to attend". Very formal - not personal.
The issue might be that if she has moved further away, she might not turn up. In which case you should just get the PSO anyway at the 48 hour hearing and they might then set another hearing a couple of weeks later.
So that's the C100 for the PSO. You need to carefully do the wording on this to state that the child should be returned and remain at the same school. It might also be an idea to make the C100 into an application to vary as well and say that if the Mother does not wish to return, then you ask that the child lives with you, remains at the same school and the Mother can collect and drop off 3 week-ends out of four and half the holidays, still under a "lives with both parents order".
So the other application for enforcement is the C79. That is for the breaches. An enforcement hearing should be about 21 days after application. But - the C100 PSO is the important one, because it can say the child must not be removed/must be returned. However, an application to vary hearing could take longer so having the C79 in as well means it could get dealt with quicker.
So I would do this:
1) C100 for urgent PSO and application to vary the lives with both parents order. Take it into court on Monday morning as soon as the court opens - ask for a same day ex parte hearing for the PSO - if they say no, then tick for a 24 or 48 hour hearing. The clerks will help you sort it.
2) C79 for enforcement. On the page where you put info, LIST the breached dates and times. Eg Friday 10th January 3.30pm until present (Sunday 12th January 6pm). The dates and times ordered when child should have been with you, but you can't post date it so it can only include breaches up to the time you fill the form in! Underneath the list of breaches write a very brief summary that you have had a 50/50 shared care order for x years, and the Mother has suddenly moved the child x miles away without notice. That you have also applied for a PSO for return of the child, and ask the court to enforce the lives with both parents order.
Sorry, I've just seen you've got no contact details for them - not even a mobile number to send a text? In which case say that in the PSO application, ask for an ex parte hearing.
Have you any idea at all where she might have gone? How did you find out she had moved? Have the school any idea where the child might be going? Did she give notice to the school? If so they should have informed you as it's a lives with both parents order (but they don't always unless you pre-empt that and specifically ask them to let you know if she ever hands in notice for the child to leave the school).
Let us know how you get on.