Do you think that their uses overlap too much, or that having both on a character is alright?

not really, you can use alchemy for poisons, enhancing smithing and enchanting, restoration is like free potions you don't have to mix or run out of.

Not redundant at all. I have a character who never uses magic, so alchemy steps right in.

Can Alchemy block spells or even shouts dead in their tracks? Can Alchemy make undead run for the hills? Can Alchemy take up no weight in your inventory?

Im talking about on the same character.

and I would only be using alchemy for potions. I won't be using a weapon.

Restoration requires mana and is most useful for healing, whereas, alchemy can make poisons, potions, and all kinds of skill boost potions and stuff and requires no mana. So alchemy could be more useful instead of focusing on both, but it depends if you want to waste time buying and getting ingredients.

This