You have 2 sets of switches administered by different groups that do not cooperate?
Or.. is there some security requirement for physical separation of these 2 subnets?
(that opens a whole other can of worms)
You'll need a "switched infrastructure" (possibly a third set of switches?) to support your APs.
If your APs are supported by one of the 2 sets of isolated switches, you'd need/want some assistance from the adminstrators of those switches re: creating a third wifi management VLAN as Michael suggested.
At that point it should be "just as easy" to create an additional VLAN to support both of your two different subnets on 1 set of switches. (in addition to the third management VLAN)
If you can't get that level of cooperation then you'll need that 3rd set of switches.
You'll have to create a wifi management vlan, a vlan for 10.10.10.x, a vlan for 192.168.0.x, plug one port from each of your isolated subnets into an untagged/"access" port that belongs to the appropriate VLAN for that network.
Attach the ZD controllers (because you're not using "standalone" APs) to an untagged/"access" port that belongs to the wifi/management VLAN.
Plug the APs into VLAN-stacked/802.1q/"trunked" ports that have their untagged/"native" VLAN set to the management/wifi VLAN.
(the other 2 VLANs also need to be allowed/"tagged" on those AP ports)
At this point your third set of switches might be able to replace the original two sets of switches.
Then (as Michael pointed out) if you want to be able to administer your ZD controllers from one of the "two different" subnets, you'll have to have a router connected between one (or both) of those subnets and your wifi management VLAN/subnet.
If your 2 different subnets were separated for security reasons, you will need to understand the security requirements and possibly buy a firewall (in addition or instead of a router) to enforce those requirements.
I hope that helps.