So far it does sound like pretty normal 4 year old stuff testing boundaries. Thing to keep in mind is that immediate timeouts are really effective and fairly easy to do. Consistency is important - so just pick one or two things and work on that. Once that behavior is changed, go to work on another one.
If the ADHD thing bothers you, a great book is "The ADD/ ADHD Answer book," by Susan Ashley. Good luck
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It is awfully tough to bring up three young children alone. Try to get some time off if you can. Maybe you have a helpful sister or aunt who can pitch hit for you. You will see things much more clearly if you are sometimes removed from the situation.
Just my two bits. Does it seem at all like it could be jealousy of the 7week old or missing Dad? You should try to work on that to see, otherwise it looks like evaluation for ADD or parenting help.