I think that it would be the X10 that would be sent into Dalton Park.
The 2 registrations that you have posted make it clear to me that they are looking to split the services to avoid the use of a tachograph. The X9 can be split at Peterlee but the X10 can't be split from the Peterlee slip-road but can be at Dalton Park, as shown by Stagecoach's X55.
RE: Go North East: Upcoming Service Changes v2