I think you are referring to Umaima, which means "young mother", Umamah doesn't have a clear meaning. As for "elder mother", there is no special Arabic word with such a meaning. Umm means "mother", and Jaddah means "grandmother".
Arabic grammar has an operation called Tasgheer where you can change many words to mean "younger, smaller". For example Khadija can be made into Khudaija, Fatima can be changed to Futaima ("little Fatima"), rajul (man) can be changed to rujail (little man), and so on. But it doesn't have a similar operation to change a name to mean "older".