I would advise some caution here, and maybe get some professional advice.
My DH, in his 40s, lost his dad about 10 months ago. His dad left his half of the house to my DH with stipulation that MiL has the right to live there - this seems to have been an attempt to avoid the value of the house being counted for assessment of care home fees in the event that MiL needs residential care in her final years (which is a totally ridiculous thing to do, as we are not going to sit on an asset worth over half a million pounds and let MiL suffer in the lowest-cost most basic care home the council will pay for, and anyway she may never need it - but that is another thread)
Anyway the legalities of inheriting half a house have been a total nightmare for my DH it has been really complicated with various unexpected issues. Also it would have completely shafted us if we weren't already on the property ladder as "owning" half this house would disqualify us from most of the schemes available to help first time buyers. It may also affect what stamp duty we have to pay if we have to move in future. The legal hoops and paperwork are still causing issues 10 months later.
You may not be doing your child any favours by doing this. Think about the consequences carefully. Do you want your child to have to cope with all this? Also think about your DH's personality - is he genuinely the kind of dick who would let his chil get dusinherited if he remarried after being widowed? If he is, divorce him now, get your half of the assets entirely separated and make an uncomplicated will. If he isn't then consider trusting him to do the right thing by your child if you predecease him?