My soon to be mother in-law wants to hangout with my mom

My parents and my soon to be in-laws are a lot different and there’s an age difference. My parents are 57 and 64 and my fiancés parents are almost 80 (he was adopted). His mother is relentless on wanting to hang out with and get to know my mother and my mother doesn’t really want to. I feel so stuck in the middle. They met at my grandfathers funeral and they spent a few hours together when my fiancé and I moved into our place. My mother is almost anti-social and kind of in a depressive state right now due to some health issues etc. His mother thinks it’s weird they don’t know each other or that they haven’t hung out. My mom doesn’t think it’s necessary and doesn’t really want to. She said she doesn’t hang out with my sisters in-laws. But, what the normal thing? For them to spend time together or not? My soon to be MIL wants to meet for lunch within the next week and I know my moms just going to be like why or maybe later. I’m so stuck in the middle and I hate it.