As you’ve configured it (“Repeater”), the LAN Gateway of R2 needs to be 192.168.10.1. Clients of the repeater have their own network and need to use THAT repeater’s LAN IP as their gateway. Instead, you’ve specified the upstream router’s gateway, which is not on their network.
But even though this is the problem, the bigger problem is that you’re using “Repeater” rather than “Repeater Bridge”. The latter doesn’t create a second network AT ALL, but instead just transparently passes traffic to the primary network. IOW, all clients of either the primary router or repeater are always on the same network, thus the whole problem w/ the gateway IP above becomes irrelevant.
Now whether you should use “Repeater” vs. “RepeaterBridge” depends on your intentions, which you didn’t state (although you mentioned not being able to change R1, suggesting “Repeater” may indeed be what you want). You typically only use “Repeater” when you want to create a second network for some reason, such as protecting yourself from another network that might be potentially hostile (e.g., an open wifi from a neighbor or nearby cafe). But if it’s just your own network, it’s much better and easier to simply use “Repeater Bridge”.
Repeater bridge does work for me. The reason I want to change to repeater is the former setup put too much load on the primary router. All device connection request is send via repeater bridge to the primary router. This I think is making the primary router very unstable. It crashes on and off.
My intention is to have the repeater router handle the dhcp service and be on a different subnet to the primary router. This way, the primary router only need to have one device (repeater) connect to it.
First, did the change in gateway IP fix the problem?
Second, I don't really see how having a second network w/ "Repeater" helps resolve the problem you described. As I said, it actually complicates access since now everyone and everything on the primary router's network is blocked from accessing the network behind the repeater, at least by default. Things like Windows network discovery will be messed up as well since that protocol always confines itself to its own network.
But putting all that aside for the moment, ultimately what's the point of the repeater? To access the internet, and which can only happen if it passes through the repeater and over to the primary router. The fact that once in a blue moon the devices behind the repeater need to make a DHCP request over the repeater and to the primary router can’t possible account for any instability. Whether you use “Repeater” or “Repeater Bridge”, those devices are still connected to the repeater and will interact w/ the primary router’s AP for internet access at exactly the same rate and in the same way.
So whatever instability you may be experiencing, it's not clear to me how using "Repeater" rather than "Repeater Bridge" helps. But ultimately that’s up to you. If you feel it does and you can live w/ the numerous other obstacles it presents, then that’s your choice.