It's possible, but unlikely, that the couple could have owned the house under a 'tenancy in common' (rather than the more usual 'joint tenancy'). Under those circumstances, it's possible (but once again unlikely) that the wife's will could have left her share of the house to the children but assigned a 'lifetime interest' to her husband. If all of those conditions were met, the original three children would each be entitled to a one sixth share of the house upon the husband's death. (That statement assumes that the tenancy in common allocated 50% of the house to the wife and that she divided that share equally between the 3 children).
However, it's far more likely that the husband and wife would have had a joint tenancy and simply made 'mirror wills'. When the wife died, the husband would have acquired full ownership of the house. At the moment of his marriage, his previous will was invalidated. If the husband now dies intestate, his new wife will become the outright owner of the house. If she then dies intestate, the original children would not have any claim to the house. However, if the new wife dies first and then the husband dies, it's likely that each of his 5 children would be entitled to a one fifth share of the house.
I used to write wills for a living and I've tried to keep that as simple as possible. However, every time I've typed a sentence I've wanted to add 'but' or 'if' at the end of it! I can only hope that the husband and wife both write wills or things could get very messy!
Chris