Its Master parent> child> child of object2

I just basically wanted to get all the Id and names from the Child of object2.

Tried this but I am getting 'Unknown error parsing query' SELECT Id, name (SELECT id, name FROM child of object_2) from child

completely "bottom-up"

SELECT Id
FROM Child2__c
WHERE Child1__r.Master__c = '...'

or you were close

SELECT Id, Name,
(SELECT Id, Name FROM Children2__r)
FROM Child1__c
WHERE Master__c = '...'

(but for this you'll have to be sure what's the relationship name between child1 and 2)

Edit after OP provided exact relationship names

Bottom up would be

SELECT Id, Name
FROM Event_Expense_Detail__c
WHERE Service_Order__r.Ford_Field_Event__c = 'one master id goes here'

You start from the lowest point (detail) then go "up" with dot notation once to Event Expense and then "up" again. If you still don't feel it - try

SELECT 
    Service_Order__r.Ford_Field_Event__r.Id, Service_Order__r.Ford_Field_Event__r.Name,
    Service_Order__r.Id, Service_Order__r.Name,
    Id, Name
FROM Event_Expense_Detail__c 
ORDER BY Service_Order__r.Ford_Field_Event__r.Name, Service_Order__r.Name, Name
LIMIT 100

Top-down is limited, you can go 1 level down. So we'd have

SELECT 
    Ford_Field_Event__r.Id, Ford_Field_Event__r.Name,
    Id, Name,
    (SELECT Id, Name FROM Service_Order_Items__r)
FROM Event_Expense__c
WHERE Ford_Field_Event__c = 'one master id goes here'