You need to follow a fair redundancy procedure. That means looking at the correct pool from which you will be selecting the redundant employee. It seems clear to me that you have a pool of three.
The fact is that you require two full time jobs to be done. Query whether that requires two full time employees. You must consider whether you could you operate with one full time and two part time, or even four part time staff? You may say not, but you must think about this and if you decide you cannot operate the new structure with part time staff you will need to be able to justify that decision.
You should not assume your part timer won’t go full time or indeed re-locate, hence it is very dangerous just to limit your pool to the part timer. This will very likely be a breach of the Part Time Workers regulations. With regards to relocation, yes, if they want the role, are suitable and better than at least one of the other two employees, relocation may be necessary. However, unless your contract or relevant policy says otherwise you are not obliged to pay someone to relocate.
Your next step will be a selection process based on objectively justifiable and measurable criteria. Part time status is not a selection criterion.