70s/80s Arcade Game Like Galaxian/Galaga Where You Dock Your Ship Twice: It's Xevious
You're describing Xevious (Namco, 1983).
Why It Matches Your Memory
Docking Mechanic: The player ship (Solvalou) docks with a mothership twice per stage—once to recharge energy, once to receive the "Zapper" air-to-ground bomb upgrade.
Vertical Scrolling Shooter: Like Galaga/Galaxian, but with a continuously scrolling terrain (forests, bases, rivers) instead of static screens.
Dual Weapon System:Forward shot (Vulcan) for air enemies + Bomb (Zapper) for ground targets (Sol towers, Domogram rovers).