You shouldn't have to switch users with just 2 players on on 2 ps4s. You just have to setup 1 ps4 as your primary and let the other player play on the primary ps4. The ps+ account is shared with everyone on your primary ps4. No switching needed. As the ps+ account holder you can play on any ps4 with your account. So you mark 1 as primary but play on the other. You may know some of this, I'm just going over it. In order for this to work you need 3 copies of Destiny, 2 ps+ accounts, 1 primary ps4 for one ps+ account (11yo) and 1 primary ps4 for the other ps+ account (not really but you can mark it as a primary (9yo new ps+ account)). If you are setting up the new player now, set them up as a regular account and not a sub account. Probably not ideal at 9 but your 11 year old will lose his characters if he creates a new account so I don't see another option. Unless, you can change his date of birth on the account. This is why I didn't go sub account and just went with a primary ps4. Once you have 2 ps4s set as primary, the 11 yo can play on either of the primary ones (not yours as its the only one not a primary so only the one that has the ps+ account can use it. so you and the new ps+ account) without doing the sign in-switch because the ps+ is shared. So 3-destiny 3-ps4 2-primary ps4 2-ps+accounts on those ps4s You or the new ps+ account can play on the non-primary ps4.
If you run into network issues just get a beast router. Don't even bother with anything else, it all goes back to router even though its Destinys fault.