Please try
Map[Function[FlattenAt[#, 2]],
ReplaceAll[
Normal[Merge[
Map[Function[Association[Rule[#[[1]] , #[[2]]]]],
Join[Data1, Data2]], Identity]] , RuleDelayed[Rule, List]] ]
If your data fits this pattern {date, value} if it is {date,values,...} then change Rule[#[[1]],#[[2]]] to Rule[First[#],Rest[#]] and modify the rest of the code accordingly to get the final list into the form you desire.
