"The reasons they have given is that my child doesn’t listen, doesn’t do what the other kids are doing, is always on their own agenda and doesn’t answer or turn to their name."
@LostandFounded I'm quoting your OP because I don't think anyone, perhaps, has explained the significance of these things.
First issue: play skills
In typical children, play develops in stages. Solitary play is generally seen in 0-2 year olds - they are doing their thing, and don't care what other people are going. Then they will start watching other children play. After 2 years old, they start to parallel play - they do the same things but not with their peers. Then between 3 and 4 years old they start to do associative play - playing together but not having rules they follow. At 4 years plus, they start cooperative play - everyone follows the rules of the game.
Nursery is telling you that he's playing like an under 2 year old at the age of 3. So depending on which end of 3 he is, he's at least ⅓ delayed, and up to ½ delayed in his play skills.
At the age of 3, a ⅓-½ chronological age delay is big. Unless there is a 'fixable' reason (such as glue ear), the gap tends to widen as children gets older.
Think about it - typically developing children develop typically. So they act like a 3 year old at 3, a 4 year old at 4, and so on. If a child is 50% delayed, then at 3 they are acting like they are 18 months, and a year later they've made 6 months progress, then a year later they have made another 6 months progress.... You end up with an 8 year old with skills of a 4 year old, etc.
For a child to 'catch up' they have to make more progress then a typically developing child in the same time frame. Possible, but not typical.
Second issue: Doesn't listen
Children learn actively and passively. If they 'aren't listening' it's actually an attention issue. They aren't paying attention to events around them. So they aren't picking up on what's happening, who's friends with who, what the teacher said, what other children are doing. They aren't learning.
Third issue: Always on their own agenda
Typical children display joint attention. They want other people to care about what they care about. So if they see a sheep, they want everyone else to be excited about the sheep.
I would just urge you to really think. As I said, the way you describe your DS2 is similar to my DD1. Now she's 20 and she behaves like a very much younger child.