I presume that by "router", you mean each of these is a "router/NAT/firewall" combination appliance. Most home routers include firewall capabilities, which is most likely what you're relying upon here. (Note that NAT is a connection sharing technology, but not a defense mechanism.)
To directly answer your question, if a hacker gets inside your first router A, the answer is "yes." He could install network monitoring software (such as wireshark) on machine A. He would then have a couple of options to get the traffic into machine A to be monitored.
He could reconfigure router A to mirror all LAN traffic to the hardware
port where Machine A is located (a common task when installing a
network monitoring device; many routers and switches support this.)
He could reconfigure your router A to act like a hub, automatically mirroring all LAN network traffic to all ports (may be possible with some cheap consumer routers.)
He could configure machine A to act as a router. He could install and run DHCP on machine A, assuming router B is getting its external address via DHCP it could respond that its gateway is 10.10.0.10 (machine A's address.) That way all traffic from network B would be routed through machine A, where it would be subject to monitoring.
This would only give the attacker the capability of monitoring unencrypted traffic; but it still would not permit him to decrypt the contents of https/TLS/SSL encrypted streams. It would also not permit him to see LAN traffic inside router B, so if you were printing from machine B to another printer on the 192.168.10. network, he would not be able to capture it. (At least not without breaking into router B.)