There are some things you cnas do to lessen the likelihood that such behaviour will occur, although its not 100% preventable.
1. If you are letting the rooms directly yourself, I would recommend learning about human behaviour, body language and about a range of subtle signs that people give off all the time, especially when they are lying.
People give themselves away often without realizing it and those who give off the signs that they are or are going to be trouble, need to be spotted as early as possible.
2. If you're not already doing so, ensure you run everyone through a comprenehevsive tenant assessment process. This is more than just a Homelet check. I can offer some further info if you wish. PM me if so.
3. Ensure you include a provision in the tenancy agreement about guests staying over, under what circumstances you permit them to do so and explain why you have this rule. Explaning why helps people understand the reasons and it makes it more likley that tenants will abide by it.
You should also tell them about this informally aswell before they agree to take a tenancy, so they are forewarned.
4. If possible, only let to people who have shared successfully before (parent's home and university don't count).
5. Make sure each person knows about whatever house rules you want to have, both verbally and in writing before they sign up for a tenancy.
In dealing with your case, I would consider someone who spent 2 days each week at a property to be part of that tenant's tenancy and therefore, I would divide the bills by 6.
Its very tricky to make changes part-way through a tenancy without consent and also when its a HMO and therefore, as others have said, you may have to wait it out until you can remove the undesirable tenants.
In the meantime, why don't you start redrafting your new tenancy agreement with the guests clause properly hashed out and also, a set of house rules?
This is slightly off topic but when tenants leave, you might like to consider asking each of them what they would change or improve about the home or any other aspect or rules. Its like customer feedback and this can sometimes give you tips about improving things that you may not be aware of and which can make a difference to future tenants. As long as the outgoing tenant doesn't feel that what they might say won't be construed by you as negative/complaint-based comments, you should get some honest replies.
I used to have a pre-formed spreadsheet that could calculate each perosn's share of the bills exactly based on the time they lived at the property (for new and departing tenants and for known holidays), but now I run my HMO with all bills inclusive and its saves a lot of hassle and also, makes my property more attractive as potential tenants know they can budget exactly for the next x period of time.
Natural selection is a wonderful thing
You shall know them by their fruit
Saying "Never say never", says it