Maybe the reason of A not sending when B is installed its because outlook works sometimes in order, it means it may send the emails of account A first, and if it can't send because it can't connect to the SMTP then it will not complete the task and send the email from account B.
Do the following and test
1) Click where it says More Settings
2) Click on the tab "Out Going Server"
3) Check mark when it says "My Outgoing Server Requires Authentication"
4) Check mark where it says Use samen settins as my incoming mail server"
If the settings are currently like that then uncheck the boxes and test.
Do it with just one account installed, after the first account is working then install the other one.