I have a small "problem" in my OpenVPN setup, and I'd like to understand whether the thing that I consider a problem is actually an error somewhere in my configuration of the OpenVPN server or if this is how it is supposed to work. I'll describe very briefly my home setup.
I have two separate networks, let's say the main one is controlled by a modem/router (given by my isp), the second one is obviously controlled by another router. (Please note that I want the networks to be separated, this is the reason why I'm not using the second router as a switch or the primary router in bridge mode....). The secondary router is connected LAN-to-WAN, so I have a double NAT. Obviously when I'm connected to the second network I can reach the devices in the first network, while vice versa I cannot access the secondary network when I'm connected to the main network because I haven't set any static route towards the secondary router (besides even if I wanted to that crappy modem/router provided by my isp doesn't allow that).
My main network is a 192.168.1.0/24, with main router 192.168.1.254, the 192.168.1.1 address is reserved for my second router. The secondary network is a 192.168.0.0/24 with the second router being 192.168.0.1. I know that these ranges of IPs are not suggested for the well known reasons, but in my situation I know I won't have any IP conflict knowing the addresses I have on "the other side" of the vpn connection.
Now the OpenVPN part: my OpenVPN server is hosted on the secondary router itself (IP 192.168.0.1). I have forwarded the UDP port 1194 from my main router to the ip 192.168.1.1 of the secondary router. I setup my server and clients and everything seems to be working. When I connect to the VPN I receive my correct home public IP address, I can browse the internet, I can ping the OpenVPN server 10.8.0.1.
What bothers me, is that I can ping all the devices on the primary network too, so all the 192.168.1.x devices, while I cannot ping any device on the secondary network where the OpenVPN server itself is hosted (192.168.0.x). I thought that connecting to the VPN meant to be "virtually" connected to the network of the OpenVPN server, but again, maybe here I'm wrong, it's my first time dealing with a VPN, and probably I misunderstood something. So my question is, is it normal that, once connected to the VPN, I'm virtually connected to the primary network? I'd like to connect to the secondary network, is it possible or with my "dual network" setup it is impossible?
My OpenVPN server setup has the following parameters as "push parametrs":
"192.168.0.0 255.255.255.0"
"dhcp-option DNS 10.8.0.1"
"redirect-gateway autolocal def1"
Is my problem due to an error in the parameters above?
Or maybe it is due to the lack of static routes between my first and secondary network?
Or what I want is just simply impossible?

Thank you very much!!
[OFF-TOPIC (but related) question]
Would it be possible to connect a third router (with static routes capabilities) as a switch to the first router (so LAN-to LAN, since I don't want to set the first router as a bridge and lose its routing capabilities) and setup the static route from the primary network to the secondary network there on the third router/switch (since the primary router does not allow the setting of static routes)? Would it work to make the second network visible to the first?
Thank you again!