Please don't feel bad about the emotions you are feeling. It took me a long time to ever feel "off duty" with my DD and that was even when she was with her dad. I couldn't switch off. I found that I never napped when she did as I had to be awake incase she woke and needed me. I also felt like I shouldn't not be around her all the time.
It has took me some time to realise that her Dad can give her exactly what I can and needs to learn to.
In your case, with MIL, it is good that you have the support of someone who clearly adores your DC. She offered and enjoys it and sees it as a favour to you. However, if you really aren't happy being apart from your newborn for a few hours a day, that is OK too. 
I know you say your DH said to do it, but you are welcome to say no thanks, and could get away with saying it easily "oooh, I just love her too much to possibly spend any time away from her yet" sort of comments.
Or, is it possible for you to spend some of that time with MIL and your DD? The three of you together could take her for a little stroll round the park or bath her together that sort of thing?
Don't feel bad about how you feel, please. Your DD is a very lucky little girl, three people who clearly adore her.