I think your right. The splitter box is outside underneath the eaves.
As for the analogue tuning question, when I choose to manually tune it scans through numbers 21 - 69(?) which is the analogue frequency from what I remember. The auto tuning finds the RTE stuff with no picture. Though some of the higher channels (Sony Movie Channel, ITV3 something) work.
When I picked the TV up it was working, directly connected to the aerial via coaxial. That was about 5 miles from the Blaenplwyf transmitter.
Right then, you know the TV is a UK version and you've seen it working. This is all good. Barring some kind of fault developing in the journey from one house to another (unlikely but not impossible) then it's all pointing to a signal problem in the TVs new location, or possibly finger trouble in the set-up process. Let's focus on signal problems.
The TV has a Freeview tuner and an analogue tuner. Both use the same c21-c69 frequency space. When we had digital TV and analogue TV transmitting at the same time the channels had to be spaced so they wouldn't clash with each other. There's nothing broadcast on analogue any more so that's no longer an issue.
Freeview originally launched in 1998 with just standard definition services. The transmission standard for the UK's SD services is called DVB-T. The signals are encoded using MPEG2 compression. That's the tuner that the Panasonic has got; DVB-T using MPEG2 decoding.
When Freeview added HD services the MPEG2 coding process wasn't efficient enough to compress that larger data stream of HD 1080i signals in to something compact enough to make a viable Freeview HD channel selection. They used a more efficient CODEC called MPEG4. This was incorporated in a new broadcast standard for UK digital TV called DVB-T2. New TVs now work to the DVB-T2 standard. This is compatible with the old MPEG2 SD channels which are still broadcast as well as the new Freeview HD channels.
The Republic of Ireland adopted Digital TV much later than the UK, so their engineers were able to jump straight in with a system based solely on the more efficient MPEG4 CODEC. Ireland's Digital TV service is DVB-T MPGE4. It's DVB-T because for them version one of their move into Digial TV covers all their bases, SD and HD alike. They haven't had to release a "version 2" to add HD like the UK.
Pulling all this together then, there's some commonality in the UK and Irish TV systems, and that's why your Panasonic is picking up Saorview transmissions as ghosts. The TV will do the same with UK HD broadcasts. To the Panasonic, the channel space will look like there's something being broadcast at whichever c Channel numbers your local transmitter is using for HD. It'll probably report 100% strength, but 0% Quality, that's because the TV doesn't have the required MPEG4 decoder.
So where does this leave us?
My gut reaction is still the same. In the absence of other evidence I think you've got too much signal level from the local transmitter. I'm basing that on what you've said so far....
1) The TV is a UK set and you've seen it working with local transmissions
2) Where your parents live might be a marginal area for signal. When the original aerial system was installed to pick up Freeview you said you think it required a booster. This fits with the history of Freeview being on low power transmission while analogue was still broadcasting
3) Freeview reception is subject to the 'Digital Cliff'. That's where too much signal is just as bad as too little. The boundary is a very fine line
4) After analogue got switched off (DSO), most if not all Freeview transmission powers were boosted. That means any aerial system with an amplifier installed before DSO would then be kicking out a lot of signal strength after DSO, and possibly too much for those TVs with more sensitive tuners
5) The most important element for Freeview signal reception is signal Quality, not Strength. Amplifiers only boost Strength. Amplifying by too much actually reduces signal Quality. Cutting down the Strength restores some of the lost Quality
6) The TV is picking up what I suspect will be a weaker signals from RTE. If it had an MPEG4 decoder you might even be able to watch those channels
7) The other TVs and set top boxes in the house are fine, and an STB connected to the aerial feed that you later move to the Panasonic, so it's unlikely to be insufficient signal or a cable issue
Unless there's something else in the puzzle that you're unaware of or just not mentioning then too much signal level is the conclusion that fits the facts as you've given them here in the thread.
The answer is to try some signal attenuation on the end of the aerial cable before it connects to the Panasonic TV. There would be two pieces of kit I'd get hold of if I were you. The first is a fixed level attenuator. 10 or 12dB will be fine. The second item is a 0-20dB variable attenuator. The items can be used individually or combined.
Variable attenuators are useful trouble-shooting devices. Where there's too much signal and Quality is suffering as a result then it's possible to watch the TV's own Q and S meter and see Quality go up as Strength is reduced. I suspect too that using the attenuation will also get rid of the intrusion from RTE. The two items together shouldn't cost more than £10-£15 delivered, probably slightly less, so not an expensive fix by any means.