Some people have great in-laws while other in-laws leave a lot to be desired. The relationship between a mother-in-law and a daughter-in-law seems to be the most commonly strained. If you have seen movies like “Monster-In-Law” you are well aware of the stereotypes surrounding this in-law relationship. Most are not really all that bad, but if you get a bad one it can be horrific.
For the Mother-In-Law
One of the biggest areas of argument with in-laws is parenting style. The mother-in-law raised kids and feels that she is an expert and she very well could be. However, the daughter-in-law is a parent too and needs to be able to learn by her own experience. Constantly criticizing the new parent's style is a quick way to start a war between the both of you. Keep this in mind if you are now the grandparent. This is something you should actually take full advantage of. You get all of the good parts of the kids while your son and daughter-in-law has to deal with things like diapers, pediatrician visits and sibling rivalry.
It is always best to learn by trial and error. Although it can be painful (especially to watch), it is a way of learning that will not be forgotten. You were not a parenting expert when you first started either, Grandma!
She has a mother and you have to respect this. It is great if you two love to do things together, but she will want to spend time with her mom too. Do not compete with this relationship. This is a battle you will never win.
Do not "help" your daughter-in-law by cleaning, rearranging furniture or changing anything in their home unless invited to do so. It is one thing if you are asked to help out while she is recovering from surgery/childbirth or you are asked to help out in some other way. But if you have a key and you just let yourself in to the house and start cleaning the bathrooms? You may very well find that the locks have been changed the next time you visit. If you are babysitting your grandchildren, then THAT is your job. If they are napping and you need something to do, then read a book...DON'T start cleaning! No matter how "helpful" you think you are being, your actions will be perceived as criticizing her homemaking skills and as an insult.
When it comes to relationships, you have to stay out of the relationship between your daughter-in-law and son as well. This is another battle you will lose should you wage it. You do not have to like the woman your son marries, but you do need to make nice and respect that she is the woman that your son has chosen.
For the Daughter-In-Law
Your husband's mom is someone who is important to him. You do not have to like her, but you do need to play nice. If you make your dislike clearly known, this can cause issues in your marriage. If there is a major issue between you two, you should settle it together. Keep your husband out of it.
Grandparents should be allowed to be grandparents. You may limit ice cream and you may be strict about bedtimes, but your child's grandparents will not be. They want to enjoy their grandchildren and spoil them a little bit. This is not a bad thing and it will not undo all of your parenting. If your mother-in-law takes the kids for the night, buys them toys or does other nice things, simply thank her. She does do this out of love and not to try and disrespect you. Of course, if there are issues of safety, you need to deal with that, but if it is just a matter of your in-laws gave your children non-organic carrots, or you are afraid that they won't wash their hands every 5.47 minutes, you really just need to get over it.
For Both
Set clear boundaries and respect the boundaries that the other person sets. You should take the time to discuss these with each other. If you know what the boundaries are, it is a lot easier to work within them.
Throw your expectations out the window. You need to work with how things are and not get yourself worked up with trying to make things perfect. Perfection is impossible. Make peace where you can, love always and spend plenty of time getting to know one another.
Realize that you both have someone in common that you love very much - her son/your husband. You both want him to be happy and it will be impossible for him to do so if he wants to have a relationship with the both of you, but you are constantly battling.