Hi --- Paul --Trying to leave the emotional turmoil to one side completely and being cool and calculating, I will try to help you out with the legal side as much as possible.
1) Obviously we all understand that you cannot put an old head on young shoulders and your step-daughter is running the gauntlet here as far as being caught out as a benefit cheat goes, until she realises the risks and the implications of being caught and facing having convictions of fraud and dishonesty on her record, she will simply shrug it off like an Ostrich with head in sand....so as hard as it may seem, you will have to let her find out the hard way herself or hope that she continues to get away with it.
2) As far as the Guarantor agreement goes, you are held fully liable for anything in the agreement that your step-daughter defaults on, consider that agreement, "your own" unless she is in a position to honour it. ! (sounds very unlikely).
3) If the landlord finds out about the tenancy agreement being broken, which he will, then that depends on what kind of a person he is....some don't care as long as they get their money.....some take the moral high ground and report it, so that is down to your judgement of his personality and what sort of a person you think he is. ? Although if there are noisy domestic disputes or complaints he will hardly want or feel the need to tolerate the disturbances and enforce the agreement by bringing it to an end.
4) Once/if your SD is found out and the tenancy is revoked or her payments stopped then she will have to convince the authorities that all co-habitation has stopped or is unlikely to commence again, before they will feel they have a legal duty to continue payments or rehouse her and the children and reinstate her benefits again, or at least be satisfied that her partner is not contributing to her upkeep in any means or form.
5) Emergency housing is all it implies, the minimum they have to provide by law.... if the authority have to resort to the use of that because she is unable to stay put, then that could be B&B in an undesirable building or tatty housing in a squalid area, perhaps explaining that to her might help make her alter her dangerous path.
Hope that helps a little bit, although as long as the kids seem happy and are looked after properly, as hard as it is to say, "don't worry".....try not to dwell too much on it, all you can do is let her live and learn until the day she realises what she is doing is wrong, either hopefully soon enough..... or sadly too late. !!!
It's the childrens happiness and well being that is the paramount concern as you have stated and as long as you feel they are being treated correctly, do nothing, if you feel they aren't then tell her you will report the problem yourself, and be prepared to do so.....but whatever happens don't be tempted to take the law into your own hands and punch him first, tempting as it may be.