verify that the IR sensors (a little red circle on the flash body often on the battery side of the flash) is always pointing at the flash on the camera. Also make sure that the camera's built-in flash is UP (if you are using it instead of one of the others as your "Commander". This is the reason that the Nikon flashes rotate on the body (so that the sensor can be pointed at the camera and the flash pointed at the target. NOTE: if you are using one of the other flashes as your control, MAKE SURE that it is on the hot shoe of the camera (or connected to the hot shoe with the appropriate hotshoe to strobe cable (available at Nikon or Nikon supplier for a fee)). Also, if one of the external strobes is being used as commander, make sure it is set to commander on the controls on the back of the strobe.

If you can put one in A and one in B... (and use the on camera flash as either control only or participating in the flash, it will give you greater control over each flash. Remember that the on camera flash will ALWAYS fire even if it is just being used as a trigger. The onboard flash OR the flash in the Hot Shoe, will always flash during the shoot but if it is set as control only, then it is just sending instructions to the off board flashes and not participating in the exposure. This is a common panic for people just getting started in Commander Mode.

One more thing to remember with the D610 and optical flash control. When using the pop-up as a CLS "Commander", any setting other than "--" for the pop-up flash output will almost certainly result in your shutter speed not being permitted to exceed the "Auto FP" sync setting, normally 1/200sec. (At least that's the way my D750 works).

As long as the pop-up is set at "--", the camera will permit any shutter speed up to 1/4000. Your off-camera sb910 and yn-568ex will then be able to use their HSS /Auto FP sync capabilities to light the scene, or add fill as needed...as long as they can see the Commander... and their available power permits it.

You did not say which flash is not firing as a optical remote. The optical sensor for the Yongnuo is on the front of the unit under the red cover. The sensor for the SB-910 is on the battery side of the flash. The flashes can be controlled separately by placing them in different groups. Be sure the sensors see the "Command" flash.

If you buy the Yongnuo 622 series system, you will need two yn-622n transceivers (one for every off-camera flash), and one yn-622n-tx controller for the camera's hot shoe. Using this radio system you set all flash units to regular i-TTL (just as if they were to be used on-camera), and then you set the channel and group on each yn-622n. This system does not need line of sight. Use normal i-TTL with the 622s even if you want to make remote "manual" adjustments.

Since you've had your Nikon flash awhile, I'm sure you are familiar with the settings. The following shows the correct display for using the yn-568ex as a radio remote and as a optical remote.

This will help you with groups - https://www.youtube.com/watch?v=iJTZG5yfAh4

With the 568 - you can have multiple units in the same group and they will all fire to the command set in the camera for that group (camera set group A at full power - all flash slave units in group A will fire full power). Other groups can be set to other power (camera set group B at 1/2 power - all flash slave units in group B will fire 1/2 power) - or all groups can be set to TTL and you adjust the exposure comp different for each group - depends on what you want.

I use my SB-910 and my SB-800 on light stands using commander all of the time. Commander allows you to set the light output of each of 4 channels. Each channel can have an unlimited number of strobes as long as all are compatible with Nikon's Commander mode. I have my SB-910 using flash A and the SB-800 using B. The built-in flash controls both. I can set the ev on any if the groups from -3.0 to +3.0 to control the amount of light from each strobe. You will see that you also have multiple channels to keep your strobes and camera from triggering everyone else's at an event. (We had an off camera flash class in the local camera club that became a fiasco because the "instructor" and many of the students didn't know to use separate channels. In addition, some were using pocket wizards and were all on the same channel so they were constantly triggering each other's flashes. 3 of us were using Nikon's commander mode and we were each on separate channels so we didn't affect anyone.) The point is that you already have all of the flash control hardware you need. Pocket Wizards are nice if you camera and flash don't already have a solution that you've already paid for.
Here is a link to an article that includes Nikon and other brands.
https://www.borrowlenses.com/blog/multiple-flash-firing-with-nikons-advanced-wireless-lighting-system-using-pop-up-flash/

I use my SB-910 and my SB-800 on light stands using commander all of the time. Commander allows you to set the light output of each of 4 channels. Each channel can have an unlimited number of strobes as long as all are compatible with Nikon's Commander mode. I have my SB-910 using flash A and the SB-800 using B. The built-in flash controls both. I can set the ev on any if the groups from -3.0 to +3.0 to control the amount of light from each strobe. You will see that you also have multiple channels to keep your strobes and camera from triggering everyone else's at an event. (We had an off camera flash class in the local camera club that became a fiasco because the "instructor" and many of the students didn't know to use separate channels. In addition, some were using pocket wizards and were all on the same channel so they were constantly triggering each other's flashes. 3 of us were using Nikon's commander mode and we were each on separate channels so we didn't affect anyone.) The point is that you already have all of the flash control hardware you need. Pocket Wizards are nice if you camera and flash don't already have a solution that you've already paid for.
Here is a link to an article that includes Nikon and other brands.
https://www.borrowlenses.com/blog/multiple-flash-firing-with-nikons-advanced-wireless-lighting-system-using-pop-up-flash/