Recoil would still be better than most other offerings. If your still worried about it the .357 magnum is just fine with the right bullet. I have killed 9 Indiana deer with a .357 magnum and it will kill them just as dead at shot ranges you will encounter in the flat wooded lots around here. It is not a beanfield or shoot them across the ridge rifle though, the .450 bushmaster is my go-to rifle for that but probably too heavy for your wife and kids the way mine is set up.
I have a Marlin 1894c and a Ruger 77/357 they can try out just PM me. I have factory 158 grain ammo and some 180 grain reloads. Unfortunately I don't have any .44 magnum rifles at this time however.