That's not a very good idea, it's prone to MiTM attack since LAN B is a part of LAN A. Anyone with access to the latter can control what happens between modem and LAN B. The inner firewall won't help much against a dedicated attacker with access to LAN A. If nothing else, he/she could extract sensitive information from computers inside the private network through network communication.
Better option would be to reverse the situation and limit the public LAN group inside the private LAN according to the least privilege principle. Also, you can always monitor the switch where public network (LAN A) connects to (LAN B) and potentially set up some rules against various type of scans.
It needs to be said though that neither options are bulletproof. The safest option here, if you can afford it, is to have two modems connecting to two different ISPs. One for private network and the other for public, totally separated from one another.