I have an old 240 volt surface outlet in my kitchen. I am replacing 2 bedrooms and a bathroom behind the kitchen and have 1 existing 120 volt circuit. I would like to put the 240 volt line into a new subpanel and split it into 2 or more 120 volt circuits for the back of the house. The 240 volt circuit comes off the original circuit panel on two 50 amp breakers. Can I do this?

Is it a 3 wire? You talk about 240v but don't mention a neutral. If there is a neutral then yes.. The wire will have to be #6 for a 50 amp Brk(Canada)

Can I do this?
All depends on a neutral wire being present in that 240 Volt outlet (which is often not so). If not present, you have to install a neutral wire from the original circuit panel to these 120 Volt outlets.
Note : what wire is currently used for the 240 Volt outlet? Depending on the total new expected current requirement (heater or dryer / washing machine, perhaps ?) you may have to replace the entire wiring!
;)