Thank you! That Belfast record is clearly the Eliza I am looking for. That's given me a great lead - really appreciate it.
I have a record for Denis Collins on Ancestry here:
https://www.ancestry.co.uk/family-tree/person/tree/58238411/person/32042472339/facts, including various censuses, military, death. No record of his first and second family mixing. Its seems that they were completely separate.
That 1871 census transcription is erroneous, the actual document clearly lists Eliza as being born in Mauritius and Mary Ellen in England.
Denis was in the 55th regiment so I am not minded to think that the one in Portsea is the same one - the name is not uncommon in Ireland around the time.
Really appreciate your help! Still trying to better understand context for why at least one of the girls would end up in an orphanage given she wasn't short of immediate family.