First swap around some of the cables so you can test with a known working cable.
See if the fuzziness follows the cable or stays with the 43" TV.
And try swapping ports on the splitter.
If you have an unused splitter port purchase install a terminator cap - not the same as the usual dust cover caps often provided.
Reference link:
https://www.amazon.com/Type-75-Ohm-Terminator-Pack/dp/B000AAN76Y/ref=cm_cr_arp_d_product_top?ie=UTF8
You can usually purchase smaller packs at big box stores: Home Depot, Best Buy, Walmart....
Then consider that splitter itself may have a problem. Try another splitter - even a 2 or 3 port to test.
Splitting a signal does degrade its strength: some devices are more sensitive to (or maybe more tolerant of) than others to such degradation.
Overall, the hope is to find the problem anywhere else but in the 43" TV.
Unfortunately a life on the road may be just too much vibration and something inside the 43" is not holding up.