I want to say:

"A god who protects women while they are giving birth"

So I write:

boghmoHtaHvIS be'pu' Qanbogh Qun'e'

Is this correct? Something seems strange but I can't understand what.

It's grammatical, but your confusion marks the point at which it's becoming too complex to be practical, and at which you should break things into separate pieces.

I suspect you're also imagining the be'pu' as both the subject of boghmoHtaHvIS and the object of Qanbogh. it can only be one, and the other has to be an elided chaH.

-- 
SuStel
http://trimboli.name