You're in a very sticky situation with this as your relationship is still subsisting, even though you only sleep in the same house 3 times a week and visit daily.
The Case Worker may well take the view that you are only doing this to enable your partner to claim HB as a single parent. For immigration purposes, you won't be considered as separated but also raises issues with other Government departments on benefit fraud. All information is shared and easily accessible.
You currently appear to have no way of proving you are residing at a different address for 4 days a week.
It may cost you the FLR(FP) Parent route visa. It would have been more prudent to lose the HB and apply under the partner route.
You may well have dug yourself into a very deep hole.