You can use sed to do that. You can't use a date/time range but you can specify the pattern. Assuming you data looks something like this...
Apr 25 something ... .. ....
Apr 25 sss ww aa....
Apr 26......
.
.
.
May 3 bbb ccc ddd...
Code:
sed -n '/Apr 25/,/May 3/p' input_file