Hi there
I suspect that your DD is picking up on the tension between you and your MIL. It's not always easy I know but I would suggest that you try and remain relaxed when you are with your in-laws, and your DD is likely to remain more relaxed too.
When it comes to other people, your DD is SO little still, she is just trying to figure out her place in the world. At the moment, you are safe and familiar to her, so when there are lots of new things around she will naturally look to you for comfort and security. It is a bit part of the bonding that happens between child and carer - and a lot of theorists will tell you that the bond you develop is VERY VERY important in your child's development. So, at the moment, when your DD expresses her need to be comforted by you, I think that you will not do any harm at all by giving her the security that she needs. This will change as she gets older, do not fear.
Good luck
Jo