Does leasing ever make more sense than financing if I can take the 10k down payment (for the finance) and put it into savings for the term of the lease and then use it to purchase or finance a bigger car (assuming my family will need it then)? Or is it better to finance a smaller car and if/when we need a bigger car, trade it in/sell it then?

No. Buy smaller car than trade in. Only finance it if the rates are favorable. Else, pay cash.