If you go in-out as you've shown, all your equipment has to be turned on to get the reference signal through the chain. Also, each piece of equipment will add noise and jitter to the reference. Not recommended!
Check the impedance of the external reference input for your equipment. These inputs are often much higher than 50 ohms so that you can just daisy-chain a single cable from the reference to all the equipment by using a BNC T connector at each piece of equipment. A terminator at the end of the line is probably a good idea unless one of the pieces of equipment has a 50 ohm input in which case, that can be the last piece on the chain.
A distribution amplifier is a good idea, not just for distributing the reference signal, but also for providing a buffered reference signal for various experiments. You probably don't need to connect each piece of equipment separately to the amp, but you could. Ground loops are a fact of life that you will fight with from time to time. Whether you use a daisy-chain or star-connected arrangement, all the grounds are still connected together.
Remember that when you change the output impedance from 75 to 50 ohms, you might have to derate the output. If it had eight 75 ohm outputs, it might only be able to drive five 50 ohm outputs before it overloads.
A VIDEO distribution amplifier likely has a frequency response from DC, or very low, up to 10 or even 50 MHz. An RF distribution amplifier often starts at 50 MHz and can go up to 1 GHz. Don't buy the wrong one! You can try building an amp on a protoboard, but external interference might be a problem. For similar situations, I took a metal cookie tin and mounted BNC connectors on it so I can put the protoboard inside the box.
Ed