A number of issues here.
I would be putting a complaint, in writing, to the London store because they told you that exchange in Ireland was possible and then when you phoned them back you were told you couldnt.
I would be putting another complaint, in writing, to the Newbridge store because their staff were rude and a manager refused to give you contact information for customer service.
As to whether or not Debenhams have a legal obligation to you for goods bought in a UK store to be exchanged in an Irish store - I dont know, but would imagine as its a different country they are not obliged to look after you in Ireland.
Did you overreact? Yes I think so. If it upsets you to the point of almost being in tears to deal with incompetent unhelpful staff over a £12 handbag then perhaps you should consider getting someone else to go in on your behalf - seriously, its only a handbag!