What is the title in Chinese for my half-brothers mother?

Those that share the same mother (but different fathers) are known as uterine siblings or maternal half-brothers/half-sisters.

Those that share the same father (but different mothers) are known as agnate siblings or paternal half-brothers/half-sisters. In law, the term consanguine is used in place of agnate.

Technically, your half-brothers mother is your second mother