Try getting a book, and use the search words: "spirited children" or "raising your spirited child" or "setting limits with your strong-willed child" etc. There are many on Amazon.
Also, check and see how he is doing at preschool. THIS is a new thing in his life. Is he "behaving" at school? How is he transitioning? Do you mean he is in "daycare" (not Preschool), as 2.5 years old is "early" for preschool.
Also though, at this age, they can get pretty tantrum-y and defiant. Partly it's developmental, and their ability to communicate, and their "impulse control"(a child this age does not have FULL impulse control, thus, they cannot be expected to stop and stay stopped all the time. It's a learning process), and ALSO... a toddler's "emotions" are developing too... a child does not come fully equipped with a full range of emotions from birth, nor the ability to understand it. Different types of emotions develop as the child goes through different ages and stages.
When your son is yelling.... don't respond so quickly... or tell him "Mommy's ears don't hear you when you yell or use mean words... " At other times, saying "use your inside voice" or "no yelling" THEN, go and do something else, let him yell it out... and get his yah-yah's out... then often times, the child will deflate by themselves. THEN when he is calm, go to him and talk about it or give him a hug etc.
One thing I found helpful with our daughter when she was that age... is we began to teach her about the "names" for feelings, and the facial expressions, and different ways to communicate. It will provide a child with a good foundation for later... and in our case, it made our girl very articulate for her age and in her ability to discern social situations.
Also though, we taught her that she does and can have a "voice"... we nurture communication. BUT... that we are a TEAM and a family... so if she feels grumpy, that's okay... but not to take it out on others. For example, kids DO need to vent just like adults and they have their bad days too, and they need to know that we "understand" them. Just like adults. HOWEVER, we taught our girl that if she is grumpy/fussy... she can go in her room and scream all she wants, that this is her "safe zone"... then when she feels better, she can come out. It has worked well for us.
For a child that is defiant... well they are getting more independent too at this age.... and want to be "autonomous." BUT they need boundaries... reasonably placed for their age level and maturity. Consistency is important... and it will take a lifetime for us to instill values in our children. So, it will not be a slam dunk... and too, as they go through different ages and stages... it will occur again. The main thing is to keep to your values and "rules" for the family. Equitably.
Sometimes too though, a child who is this way is just frustrated and not getting what they need, and are lacking in something. So evaluate and reflect on this too.
Sometimes, kids are just talked "at" all the time... and only given attention for their "negative" behaviors, all day. This must be frustrating for them. As much as it is frustrating for the Parent, it is ALSO hard for the child. But, saying "shut up" is not appropriate... and he will need to learn about this and how to behave.... that is "hurts" other people etc.
Is there some reason he may be so angry all the time and frustrated?
My sister is a twin as well ... and growing up she was very fiesty and spirited and hard to manage. Mostly, it's because she is such a "perfectionist" in personality and had a hard time adapting to any changes in everyday life or with any differences in how she thought things should be. She is the type that likes regularity and a schedule and everything in it's place sort of thing....if not, she has a hard time adjusting....and she can erupt in a ball of frustration. She doesn't like anything new or spontaneous. This is how she was as a child. It caused a lot of difficulty in the raising of her. Now as an adult, she is much better... but still very particular. *Just wondering, IF perhaps your son is just the more particular person in personality as well? Since the other twin is more mellow and easy going...maybe he is the opposite and "needs" more structure and regularity to his life? If this is so... he will need to be handled differently from his twin.
Each child is different.... and what works for one, doesn't always work for the other.
It could also be that he is over-tired... does he nap regularly? This is important in helping to keep children adequately rested and even keeled. ALSO, is he perhaps just getting over-stimulated? This can also trigger tantrums in children. ALSO, some children are more sensory sensitive... and this can affect their "peace" and demeanor. My girl for example, is sensory sensitive to noises ever since she was a baby. At certain times, just having too much going on and too much noise just tweaks her limits and it's too much for her and she would start to yell and get very upset.
What we did to "solve" this is we got a cute sounding "cow bell." And, whenever her ears are getting "too full" (ie: too noisy for her and she can't take it anymore or she is too tired), we taught her to ring the bell... and this is HER way to tell us, in a nice way, that we need to be more quiet. This is perfectly reasonable for ALL of us... and it's a positive method to use, for a child as well. Since we all have naturally "loud" voices in my family... this was a good way for us to remind ourselves as well, that even we as Parents are "too loud" sometimes. Not just the kids.
Just some thoughts, all the best, sorry for rambling...
Susan