I personally know at least ten Lubavitchers that their parents not only let there kids play with litvisheh and chassidish kids, but also sent them to their schools.
I myself originally grew up in a litvishe community, the only house my parents didn’t let me go to, were the ones that my parents didn’t trust their kashrus. But the ones that were approved, I did go play with.
And I davend in their shuls, and yeshivois.
Aderabeh they don’t come to my house, or to my shul.
There is no such shita in Lubavitche and we don’t mechanech our kids to hate people, or to stay away from non Lubavitchers.
Something making me think that you teach your kids to stay away from Lubavitche…..