Apple TV with MoCA and OTA Antenna

I am in the process of replacing cable with fiber optic internet feed and using my existing coax network with MoCA adapters to support network WiFi, internet and TV streaming. I plan to install an attic OTA antenna for UHF-VHF HDTV channels carried over my coax system. I want to use the Apple TV interface with my smart TVs. My question is, how can I bring the (A) HDTV antenna feed (40 MHz - 806 MHz) with the (B) MoCA data feed (1125 MHz - 1675 MHz) together from the wall coax jack to the Apple TV box to connect from there with the smart TV? Both (A) and (B) will be carried to the coax cable jack in the wall behind the smart TV. I need to get each signal in the right format to the Apple TV box. Can I use a MoCA compatible coax splitter at the wall coax jack for (1) sending the MoCA signal via coax to the MoCA adapter and from there to the Apple TV box via ethernet, while simultaneously (2) sending the HDTV signal via coax to a coax-HDMI converter, which then connects with the Apple TV box via HDMI? In other words, can the Apple TV box manage these different signals simultaneously from both ethernet and HDMI sources? Thanks.