Do you have to instruct the Solicitor who has made the Will to obtain the Grant of Probate and administer the estate?

No, you can instruct the Solicitor of your choice and you do not have to use the Solicitor who has drafted the Will.  Your Solicitor will notify the Solicitor who is holding the Will that they have been instructed to obtain the Grant of Probate and administer the estate and request they provide a copy of the Will.