One of the first words I taught my daughter, was the word "compromise." She understood. Do not be afraid, of teaching your child, succinct applicable "vocabulary."
Teach him: fragile, danger, will break, careful, only for adults etc.
Or put the DVD player up high, where he cannot touch it.
Or get him a cheapo tape machine/boom box, that he CAN play with.
Think of alternatives....
If he tantrums because you are busy... say "I"m sorry son, but Mommy is busy, in a minute..." then go and do as you need to. He will tantrum. He will stop. A child WILL deflate on their own. Then when you come back after a minute of doing your things, say "Mommy is back! THANKS for understanding..." and hug him. Give him a positive reaction, when you return to him etc.
He probably also feels that since you have a baby... that he needs attention too and it is a reflection of his age. He need to have his own routine, too. Daily. Just HIS routine... and time. Juggling 2 kids is not easy... but it is doable.
Make him 'special' and tell him that... have a special 'wink' or hand-shake that ONLY the both of you do. That is what I did, with my eldest child, when I had my 2nd child. Get creative... make him realize, that you do 'understand' him, and 'hear' him... but some things, are not immediate.
You cannot possibly give in to each single tantrum.
A toddler tantrums... because of lack of being able to articulate what they mean. They also tantrum out of frustration... or they want to do things, which in their mind they can, but they cannot ACTUALLY do it.... cognitively nor coordination wise. Their motor skills...are still not fully developed, for example.
A Toddler, does NOT know how... to mange themselves, automatically nor instinctually. Many adults can't even do that. So, keep relative, what your "expectations" are, of your child. Age appropriate expectations. Otherwise, frustration will keep occurring for both you and he.
Also, their emotional development is STILL not fully developed. Thus, they do not completely understand their emotions, nor expressing it in a a palatable way.
So.. teach him. Coach him on it. Teach him about 'feelings' and the names for it and HOW to say it. Toddlers need that and to be given succinct examples... and role playing it. It takes time, for them to master this ability.... they are developing.
A toddler, is like a lump of coal.... not a diamond yet. So you have to help them shine.
Teach them the skills... to "manage" their emotions and expression... and that you "hear" them.
In time... you will build your child's "emotional IQ" and ability to navigate themselves in social situations and their own emotions.
So along with teaching them "boundaries" and "manners".... you also, not just 'punish' them... but you need to teach them... "how" to manage and navigate their reactions... their coping-skills, their problem-solving ability.
If he is mad for example, that's okay. Adults get mad too, right? But teach him alternate ways of expressing it... ie: letting you know in words, letting him yell in his room then cool off and you both talk about it, teaching him other words to say and HOW to say it in palatable/pleasant ways etc.
But remember.. .at this very young age.. they will not be 'perfect' about it yet. So... allow for a learning curve about it all.
It is a big ball of wax... for a Toddler, to master.
Even some adults, don't have their emotions/reactions mastered, yet.
For my kids, when they are upset/tantrum... I ONLY "expect".. that they "try their best." For them, for that situation, for the reason at the time. I do NOT expect them, (and I tell them this), to be "PERFECT" about it... but to at least show me, that they are trying. Then, I praise them. Or, if they are having a hard time doing that... I tel them they can tell me, and not feel bad, or inadequate. I tell them, that I have faith in them.. that they are trying. I make it attainable for them... and human.
all the best,