ArcPy string concatenation with both forward and back slashes

You can use !Var2!.replace('<problem char>', '<replacement string>')in your calculation to modify the value held in Var2 as needed.

I could easily be wrong on this one and what you're trying be valid, but I've only ever seen examples for or personally used a calculate field expression that is a single string. As I understand it, the string provided here is passed in and then parsed, so it can contain strings itself as long as you use single quote for the outer and double for strings within it, or the reverse... or you could use triple quotes, look up python docs for more on that, or ask and I can probably find it and point you in the direction.

Try: arcpy.CalculateField_management(TargetDB, "myfield", "!Var1! + '' + !Var2!", "PYTHON")

There may still be something else in there causing issues, but I'd try that first.

Field Calculator and python interpreter are different tools. The former post-process what you introduce as expression and should not be treated "strictly" as a python interpreter. The error message says once processed, Field Calculator tool treats your code's + "" + as a code line continuation character (i.e., , for more details have a look at https://stackoverflow.com/questions/53162/how-can-i-do-a-line-break-line-continuation-in-python). In fact, '!Var1!' + '' + '!Var2!' is converted to !Var1!!Var2! (you can verify this by copying this to Field Calculator).

To correct this error you need to thread string expression more carefully in python interpreter. For example, '!Var1!' + ' + "\" + ' + '!Var2!' will work. If you evaluate this, it turns into !Var1! + "" + !Var2! which just works since it is a valid Field Calculator expression. Personally I find python string formatting utilities better suited and safer to generate expression, e.g., r"{} + '' + {}".format('!Var1!', '!Var2!').