Oh! New baby? Ahh, that changes everything, doesn't it? All bets are off. Just be thankful that you haven't had to throw out every piece of furniture in the house or wrap it in plastic because of "frequent accidents".
When my son turned 3, the baby brother showed up, and the VERY NEXT WEEK, he was starting a new school. What a disaster THAT was! The potty training nose-dived, the super well-behaved kid morphed into a walking time-bomb, and (after several months of misery) we ended up having to take him out of school completely that year. Angry, angry young man! But he was always sweet and protective of the baby sibling, so I figured it was still an overall win.
For my kid, the whole first YEAR or more was all about adjusting to the new baby, and he LOVED his brother, so I know can be even worse for some families. We didn't realize all the... issues were due to the baby until much, much later. We thought he was just turning into an angry, spoiled kid, and we thought we had to "fix" that. If we had been more patient and just chilled out, it probably would've passed sooner. My advice is to step back, chill out, and relax. And let him know you think he's a great kid and that you love him.
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I think you may need to step back and consider that maybe he really *does* need help. Writing is quite difficult for most small children to do, more difficult than many adults realize. Try this excercise: try writing SMALL, neat letters with your left hand (if you are righthanded). This is just to remind yourself how difficult it is, and it's even harder than that for him, because you have a lot more general manual dexterity that you've built up over decades.
It takes a long time to develop the muscles in the hand that control the fine motor skills, which is why kindergarten is when children are generally taught to start learning to read and write. Preschool handwriting is definitely pushing the envelope a bit. However, there are lots of fun ways to develop those fine motor skills - PLAYDOUGH being at the top of the list! Also try using safety scissors, using salad tongs (the kind you see at salad bars) to pick up cotton balls and move them form one bowl to another. When he gets good, move to smaller things, like using tweezers to move rice one grain at a time. (Kinda like the Operation Game). (The tongs and tweezers are a Montessori trick - someone else mentioned Montessori. You'd get lots more ideas from a Montessori book, too.)
My son's preschool teachers were a little concerned, too,
that his writing skills were not quite up to speed as some of the other kids. However, he was by FAR the youngest in the class AND he was still using both hands to draw and write (ambidexterous), which slows them down in the beginning, but is REALLY useful when they get a little older. But we talked about it at a teacher conference and came up with some FUN ways to practice fine-motor skills that didn't involve writing letters, which for him was frustrating and boring. (They were also really pushing him to do more handwriting practice on his own, and he was starting to hate the Handwriting Without Tears workbook.)
One idea was to give him safety scissors and have him cut little pieces of construction paper into confetti-sized pieces and glue them onto a paper plate, like a little mosaic. He enjoyed it so much, that we did it a lot. (Although he was all about the cutting, not so much the gluing, so it left bits of paper all over the floor.)
Paper folding is good, too, although most origami books are too difficult for that age - I think Kumon makes one for little kids, but I want to stick mostly with things that are inexpensive. You could try folding paper fans.
And of course, coloring, painting, dot-to-dots, hidden pictures, tic-tac-toe. There's a lot of things you can do with paper and pencils that are more fun than drilling letters, but they still build that "muscular memory."
KEEP IT FUN! When you get right down to it, there's no need to push writing if he's not getting into it. Obviously some parents do push and get mixed results, but don't compare him to other kids. The skills a preschooler REALLY needs are more self-care, like being able to take on and off thier own jacket and shoes, and be able to sit (relatively) still and quiet for circle time, be able to share and take turns. Things that they can do at home would be put away dishes and clean up messes, get out their own cereal and bowl and pour the milk, and brush their own teeth. And all of those things are learning independence, too!