My name is Lisa Deckter. I believe am a member of the "missing" side of your family that you've been looking for.
My great grandfather Louis Deckter and his wife Ida stayed in Philadelphia while his brother Abraham ended up in New York.
I just recently found the missing brother's name - Harry Decker through ancestry.com combined with a few other websites (I can elaborate more on the details of the "trail" I followed to find the information if you like). And then bang - I found your post which confirmed everything we knew combined with what I had discovered.
My grandparents Sam and Bella Deckter had gone out to California and visited with his (my grandfather's) cousin Sam Decker, I believe it was not long before my grandfather died (which was in 1980). Since then we have lost touch with your family.
My father and his brother have always been very interested in finding the "lost" (at least temporarily) side of the family. I know he had at one point looked on Ancestry.com, but it the end it was the computer professional (me) that wins the "I found them!" prize :).
Please feel free to email me at LDeckter@yahoo.com
(and please remember the t in my last name). Any more personal information (such as more details on our family or whatever else), I can give to you in an email.
I look forward to hearing back from you.