"We don't have much in common anymore." is correct.
"We have a lot more in common with my friends than with my family." is theoretically grammatical, but the logic is off. You start off with "We" then shift to "my" and "my." It should be, for example, one of the following:
"I have a lot more in common with my friends than with my family."
"We don't have many in common with my younger sister anymore." is ungrammatical. You start off with "We" and then shift to "my." And "many" is not used correctly. This sentence should be, for example, one of the following:
"We don't have many things in common with our younger sisters anymore."
"I don't have many things in common with my younger sisters anymore."