Yes. If the OP’s children inherited the house it legally becomes theirs at that point. If the OP’s husband is given a lifetime interest to live in it then they now own an asset they cannot sell, which makes them liable for second-home rates of stamp duty on any purchase of a house for themselves to actually live in.
All assets are subject to CGT from the point where ownership begins until the point where they are sold unless there is a specific exemption as there is for a primary residence. All the time the OP’s husband remained in the house after her death the children would be the legal owners and it would not be their primary residence (given they do not live there at all) so of course the increase in value in between would be subject to CGT.
There’s no way CGT is going to decrease in the foreseeable future, realistically. There have even been floated barmy policies about attempting to apply CGT on top of inheritance tax to assets at the point of inheritance and removing the exemption on death to avoid this effective double taxation (it would make more sense to abolish IHT and apply CGT to inherited assets instead, but there we are); and even more nutty economic illiterates suggesting the exemption on primary residences should be removed meaning hardly anybody would be able to afford to move house at all.
CGT has always applied to all assets unless specifically exempted and an inherited house in which you do not live and has been owned for years before you can sell it because it’s still occupied by your parent’s partner is not one of those exemptions, never has been and is very unlikely to ever become an exemption.
As multiple posters have explained, the sensible option here is not to marry and not to cohabit either. If they are determined to cohabit then the OP’s best option is to rent out her current home and rent or buy a separate property with her partner jointly, leaving a clear will that any equity in that new property if they choose to buy (assuming that they put down equal deposits - and she can do this without taking out a mortgage on the existing house - and that they pay the mortgage equally) will go to her new partner but everything else to her children. And not to even considering marrying him: it would be madness to do this at this stage in life and potentially financially ruinous for her in the case of divorce, aside from the very real prospect of accidentally disinheriting her children.