In my experience, yes she can get the LTR heard at the same time at the contact application, although shes highly highly unlikely to get it resolved in a 10/15 minute Directions hearing. What most likely will happen is directions will not only be given about how to proceed and investigate contact but also the LTR. Its quite frequently takes 6 - 12 months to resolve!
However if she is moving on the 26th July surely shes already gone before the directions hearing? Is she prepared to travel back for the hearings?
The complication I see in this case is that you and your partner are also moving out of the juristiction arent you? So is it that you are contesting the LTR because you want her to remain here or you are happy for her to relocate subject to contact being agreed?