He just started Kinder I assume.
His Daddy is not home.
He has a new schedule/new life's demands now. School.
He is adjusting.
A young child spends all day in Kinder, being spot on and doing things and following direction and being in structure and getting over stimulated. It is like work. It is 'work' for them. Kinder is not all just playing all day.
They are tired after that.
After school, kids are tired/spent/fatigued and often hungry. All of that, combines to make for a kid, that needs to deflate. If not, they get, fussier.
And they let it all hang out, once home.
Deflating.
This is common.
After school give him a snack. Because, low blood sugar, often will also make a child fussy/hard to concentrate/impatient etc.
Especially if they do not eat lunch, at school, even if they have food. Many time, kids do not eat at school. Even if they have a lunch. Its adjustment, they may not like what they have to eat etc. and are hungry.
He is, deflating, at home after school.
They get cantankerous.
My kids, after school, when younger, did that.
So, after school, I let my kids just hang out and relax. I don't make demands on them right away. I let them relax, eat a snack etc. Unwind.
Then, they feel better.
And, kids still may need a nap at this age. My son does. My son is in Kinder. When he is tired, he actually gets more hyper... and boisterous and fussy. I KNOW that is his cues, for trying to FORCE himself awake, although he is tired.
My son, is napping now in fact. He was SOOOO tired after school today.
He needed it.
If not, he would have been very fussy as the day wore on and by evening. And when tired, my son can't even eat, even if hungry.
So I know, his cues.
For your son, I doubt putting him in daycare after school, will make a difference. Because, he already had a DAY of school/Kindergarten. And prolonging that day, to become even longer... will tire him out, even more.
To me, and per my kids and my friends kids... this is what the 'problem' is.
This is what would tweak my kids, after school.
You are a SAHM. So being with your child, spending time with him, to me, is not a reason.
The reason is: he is now in formal school. It is a BIG adjustment. Kids are, really tired and fussy after school. They are young.