That 3 night thing is urban myth.
And under TC and HB rules ex partners are allowed to be at yours for baby sitting.
HB wise if he is maintaining different housing and using it as a house none of the rest matters.
TC wise if the above applies and you are not taking joint responsibility for your household not making future plans (holidays together ect) every thing has changed to his new address,he is not treating your home as his own,other people know you are single that sort of thing then you really do not need to panic if during baby sitting he cooks the kids meal or has a change of clothes (he is baby sitting over night it's not unreasonable to need to put clean stuff on).
They are not even allowed to ask you if you have sex nor where he sleeps.
When you read the manual each section has to be read in conjunction with the others no one bit is stand alone (behaviour wise) it would not be one action alone that would end up with a LTAHAW result it would be rather a lot.
E.g separate households,no financial links,no mailing lists,no joint responsibility for household, stays over for baby sitting has toothbrush and clean boxers/socks does his washing at home, wouldn't be a problem
Living under same roof but totally separate,everybody knows not a couple,no socialising (unless for carer reasons) each does own household chores so no joint cooking/cleaning/laundry and no joint financial responsibility could cause a problem but shouldn't and would be found not to be if appealed.
However the vast majority of stuff these days is done by data matching they have usually made their decision already (even if that's not what they should do) before they even contact you and have been known to ignore explanations so its always best to check and double check that data matching stuff is up to date