Okay, so it looks like the inheritance and the proposed transactions aren't decades or years apart.
The first tax issue is possible CAT due at inheritance.
If the two adult children A and B have not used up their category A allowance, then there isn't any CAT due on their inheritance.
By the way, do either A or B live in this house?
Then, secondly, after that, you are asking what is the most tax-efficient was to transfer 100% ownership to person A or person A's child.
If these transfers occur soon after inheritance, then there shouldn't be any capital gains, so CGT does not arise.
(1) A buys half from B, pays the market price 95k - I can't see any tax implications here, other than stamp duty
(2) B gifts half the house to person A. Here, person A, you, will face a CAT bill, but of course you won't have paid for the half share. May also be stamp duty.
(3) Both A and B gift the house to child C. The child can get half free of CAT, and then it looks to me that the child would face CAT on the other half.
(4) if both A and B sell the house for 190k, the same value they inherited it at, then there is no CGT due.
This is complex enough, so I would wait for other posters to contribute, as I am not an expert, or else ask a sol.