How do I compete with my daughter's rich mother-in-law when she prefers to be with her because she gives her more material things?

I have this issue with my parents and my children. I found that making memories are far more valuable to my kids. I take them to the beach, park, or on mini-vacations to keep them from preferring more time with my rich parents. Additionally, I watch movies with them, play board games, and set up fun dance parties with goofy costumes to keep them home with me. I also started doing this happiness list where we talk once a month about the things that would make them happier. One of the things on the list is Taco Tuesdays and Dance Party Fridays.

Know your daughter well. While it may not necessarily be materialism that's the reason behind your daughter's liking for her mother-in-law, it may be that gifts are one "love languages" your daughter listens to. (I suggest reading about Chapman's Five Love Languages on the internet.) Notice which love language she listens to (it may be different from the one she "speaks" with). If she really likes gifts, consider which kinds she likes and look past the price tags. What is she interested in? Is it really the object? Or something about the object? Or the fact that the giver understands her well enough to know what she likes?

Don't compete with her. Talk with your daughter about your feelings. Tell her how much you love her.

The competition sounds like it's over material things. This may sound cliche, but those things are just things. They cannot replace love, respect, time, appreciation. Your daughter's mother in law may have financial footing to lavish gifts on her...But giving gifts isn't the answer to being the better person. It could also be that her mother in law, that's the way she expresses her love for your daughter. Your daughter may also have receiving gifts as a way of feeling appreciated. A good chat about how you feel tossed to the side or you're in competition is something to consider because it sounds like you and the mother in law both care for your daughter-- BUT it seems there is some miscommunication.