My 3 year old is playing up lately too. I think is just the age. They realise they can push you & test their boundaries & will do anything to see if you are true to your word.
All the advise I can give is to stick to it & be consistent. Try to always remain calm too. Flying off the handle doesn't help.
They should grow out of it soon. Well they bl00dy better! I'll go mad other wise!
Sorry I can't help much, but just know that you aren't the only one.
How long do i stick to it each time thats the question??? he could easily go hours i know he could!!!!

As for involvement with baby he does all the nappies gets them and puts them in bin along with getting wipes and nappy covers. He kiss's baby daily and holds his hand and helps where ever possible. He even gets blankets dummies and out fits mostly he does this of his own bat