Hi @synrst to add to the other answers, I wanted to clarify if this was going to be a true mesh link between two APs or if you're just hoping to have the wireless client device at the far end. From your description it sounds like a true wireless backhaul link between two APs, the house is the gateway AP and at the gate you have the mesh AP, with the camera getting back over that backhaul/mesh link.
Like @Ryan_Miles said the MR78 isn't intended for this purpose, but might actually work "good enough" given the 260-foot distance. So yes, this can work, but perhaps not that well, possibly not at all, and if it does it's much less than ideal. When we have typical outdoor mesh networks with MR76/86 and ANT-20 omni antennas, we typically stick to 100 to 200-foot max spacing.
That said I'd also be inclined to recommend MR76 as @PhilipDAth mentioned for this purpose, with a band-specific sector antenna like the ANT-21 5GHz sector antenna. This way you could ensure the APs will choose the 5GHz band for mesh backhaul (they would anyway because you're using the 5GHz ports on a 76) and you can manually configure a non-DFS 80MHz channel on a 5GHz-only SSID for the mesh link. If it's an MR76 you could also leave the 2.4GHz radio turned off and put some weatherproof 'N' caps over the 2.4GHz ports.
And you may actually only need an MR76 on one side, which is not typical design practice, but you would have antenna reciprocity going for you. What I mean is if you have an MR76 and ANT-21 out at the gate, that is going to both transmit and collect a lot of signal to/from the MR78 on the house and give you a better reach and SNR scenario versus if it was 78-to-78 (omni-to-omni). Or the reverse, depending on mounting options or aesthetics, you could have the MR76 and ANT-21 on the house and an MR78 out at the gate.
This is all assuming the camera is not wireless capable? Because if this was a Meraki MV camera or any other camera that has wireless capability, I'd advise no mesh link and no AP at the gate. Rather a single MR76 or 86 on the house with sector antenna(s) aimed at the gate, that would be no problem at a few hundred feet for a wireless device at the gate to associate directly back to the house AP. But it sounds like the scenario you are describing is that you might have a wired camera and would have to get it's wired connection into the mesh AP to get back over the backhaul.
Hope that helps! Ping us back for follow up.