You need a solicitor who is experienced in probate and wills.
One thing that is apparent is that removing an executor by court order is normally only done after probate has been granted and on the grounds that the executor is failing in their duty in some way. It requires an application in the Chancery Division of the High Court. (There is, in fact, nothing in the wording of the section of the Act, s50 of the Adminstration of Justice Act 1985, that says that an executor cannot be so removed before probate is granted).On the face of it, this is not a suitable procedure in your case.
There must be other, simpler, methods of proceeding. You solicitor will advise . They are likely to have encountered this before.
There are certainly time limits involved here: for example the executors are supposed to get an application for probate within twelve months of the date of the death, which means that they'll have had to prepare accounts of the deceased's income and property and pay any inheritance tax. You don't say when the death was but patently time is running
Furthermore, not only are you an executor but you are also a beneficiary. Beneficiaries are persons interested in the estate and have a right to receive the property due to them in proper time.
.The easiest answer may be for your sister to renounce her executorship, simply stand down, leaving you to administer the estates.It may be that she can be so persuaded.You may know why your sister is behaving as she is.It could be she just can't face the responsibilities, keeps avoiding facing them, but also thinks that she cannot get out of being an executor. She might be relieved to find that she could stand back.Your solicitor should be be able to help and advise on that too.