Database

db={"A":[{"parentCentre":{"$oid":"1cbafa99d8c77251bea30f11"},"childCentre":{"$oid":"5cbafa99d8c77251bea30f8d"}},{"parentCentre":{"$oid":"1cbafa99d8c77251bea30f11"},"childCentre":{"$oid":"5cbafa99d8c77251bea30f8d"},},{"parentCentre":{"$oid":"1cbafa99d8c77251bea30f11"},"childCentre":{"$oid":"5cbafa99d8c77251bea30f8d"},},{"parentCentre":{"$oid":"1cbafa99d8c77251bea30f11"},"childCentre":{"$oid":"5cbafa99d8c77251bea30f6d"},},{"parentCentre":{"$oid":"1cbafa99d8c77251bea30f21"},"childCentre":{"$oid":"5cbafa99d8c77251bea30f6d"},},],"B":[{"_id":{"$oid":"1cbafa99d8c77251bea30f11"},"Type":"Parent","Name":"Kris Labs"},{"_id":{"$oid":"1cbafa99d8c77251bea30f21"},"Type":"Parent","Name":"DEX Labs"},{"_id":{"$oid":"5cbafa99d8c77251bea30f8d"},"Type":"Child","Name":"Mili Labs"},{"_id":{"$oid":"5cbafa99d8c77251bea30f6d"},"Type":"Child","Name":"Max Labs"}]}

Query

db.A.aggregate([{$group:{_id:{p:"$parentCentre",c:"$childCentre"},count:{$sum:1}}},{$group:{_id:"$_id.p",Records:{$push:{childCentreName:"$_id.c",recordCount:"$count"}}}},{$unwind:"$Records"},{"$lookup":{"from":"B","localField":"_id","foreignField":"_id","as":"p"}},{"$lookup":{"from":"B","localField":"Records.childCentreName","foreignField":"_id","as":"c"}},{$unwind:"$c"},{$unwind:"$p"},{$project:{"parentCentreName":"$p.Name","Records.childCentreName":"$c.Name","Records.recordCount":1,_id:0}},{$group:{_id:"$parentCentreName","Records":{$push:"$Records"}}},{$project:{"parentCentreName":"$_id","Records":1,_id:0}}])

Result