@eta's advice is good.
Where you've run your own cable then we shouldn't really need to worry about the poorer shielding of old analogue-era coax. Next is the quality of the ancillaries such as the wall plates if in use.
Good quality shielded wall plates have a metal housing that covers the signal cable connections. Poorer-quality unshielded ones, (and often sold at inflated prices online) have a simpler clamping mechanism that leaves the cable ends exposed. Where there's a source of interference such as a bad switch-mode power supply then the unshielded wall plate can be a real weak link.
Coax fly leads are another common backdoor for interference. I'm talking about the moulded ones sold by the likes of supermarkets, Argos, the DIY sheds etc. Again though, where you've run your own cable then you should also have made up your own fly leads too. As long as the plug ends are fitted well-enough then these shouldn't be an issue.
Presuming you've checked all the plug end fittings, and no one has banged a nail through your cables or crushed/trampled/kinked or cut a cable, then what remains is the the amplified splitter.
Does yours have a socket marked something such as
FULL or
FULL OUTPUT?
If so, and you're using that one to connect to the TV that has issues, then that could be the problem. The TV might be getting too much signal. With digital signals, this can create what looks like the same issue as low signal strength/quality. What happens is that when the signal is too strong it overloads the tuner and it looks like the Quality measure goes down. The fix for this would be to use an attenuator to reduce the signal power going to the affected TV.
I don't know if this is the situation in your case. We are not onsite to see things first hand, so all we have is the info you've given us. This then is a process of elimination based on dealing with the most likely causes first. It's a troubleshooting process when working largely in the dark. I hope you understand?
Once we rule out all the above, then the next stage is to do some signal connection swapping. Go up to the amplified splitter. Swap the feed to the affected TV with one to a TV that is known to be good. Check if the problem stays on the same TV or if it moves to the other telly.
Where the problem stays, then it's a cabling issue or a problem with the TV tuner itself. Where the problem moves, then it's most likely an issue with the amplified splitter.
Try the things suggested and then come back to us with an update.
As always, if this or any other answer helped, please click the THANKS button on those posts to show your appreciation. It costs you nowt to do and is quicker than typing a post with the words "thanks" 
