"Har på seg" literally translates to "have on oneself." There is no word for "wear." You have to have the second dere because it's replacing "seg."
Jeg har på meg = I have on myself.
Du har på deg = You have on yourself.
Vi har på oss = We have on ourselves.
Dere har på dere = You have on yourselves.
Han har på seg = He has on himself.
Hun har på seg = She has on herself.
De har på seg = They have on themselves.
In English, I guess you COULD say "I have on a sweater," even though it's awkward. In Norwegian, it's just not grammatically correct. You have a preposition with no object.
I, who has been accused of being very adroit with English and the various nuances of its usage, would say "I have on a sweater," or, more likely, "I have a sweater on," if I wore sweaters.
I have on (right now) pants, a shirt, and underwear. I'm not wearing any socks. I also tell my kids, on cold mornings to "Put on a …"
Here you specified, in the same sentence, your kids as a one subject.
Therefore, "Put on a jacket" in English having the hidden subject of 'you' would be more like "(You) Put on a jacket." Since you stated your kids, you are directing that 'You statement' ,as I learned in highschool, towards your kids so it would be understood as "(Kids) Put on a jacket"
In Norwegian, there is no such thing as a you statement.
"Dere legger på dere en jakke" Or "Dere har på dere en jakke"
Basically translating to: "You put on (yourselves) a jacket." Or "You are wearing (on yourselves) a jacket."
'Dere har på dere' is needed instead of 'du har på deg' because yiu specified 'kids' which is more than one and you are using such 'you statement' towards them. Had you been talking to one single child, "du hapå deg" qould be accepted.
It's being used like a reflexive verb from what I can tell (bearing in mind I'm learning all this too), where it's not an exact translation between the two languages. So you're not saying who's sweater you're wearing, you're saying a sweater is on you. You would need to use a possessive to indicate ownership of the garment since the verb is saying who's affected.