Connecting two amps wirelessly?

Hello. My family owns a cafe, so I'm helping them out with technical stuff. They have both indoor and outdoor seating. We want to play the same music inside and outside, but there are no cable conduits of any kind (brand new governmental building with "hermetically sealed" fasade - windows over many floors). It has revolving doors, so cables through the door is not an option.
We use two normal home hi-fi (Onkyo) receivers with two iPads (one indoor, one outdoor), cabled speakers. Setup is simple to operate. But we need to connect them together without any lag.
I want to split the indoor iPad (to the indoor amp + the wireless transmitter). Then outside amp with a wireless receiver. Alternatively feed the indoor iPad signal into just the wireless transmitter, then attach receivers to both the indoor and outdoor amp. If both amps are on indentical receivers (BT mesh?), they won't have any lag between them.

Any suggestions on what to buy?