On the positives you are going into their home aware that it can cause problems. I agree with the poster up thread who suggested you sit down with your family. As this thread has shown, people have different ideas, the best people to ask are those who it affects.
Has your DD & SiL proactively offered to take you in or is it a reluctant agreement while you have no where else to go, as that can make a huge difference.
Devise a plan to manage expectations and a timeline. How much can you contribute financially and on a practical level, and what is the routine, where would you fit in, that sort of thing.
On the practicalities of housing. Are you being evicted, can you afford your rent? Have you had support to claim discretionary housing payments whilst you look for a different place to live, contacted Shelter or housing support? A rent top up could give some breathing space while you looked elsewhere and reached the stage where you could maybe increase your hours.
Have you looked at renting a room somewhere else or in over 50's housing which exist in many arears? If you are approaching the council you need to ensure you are not classed as intentionally homeless.
If your Mental Health is so poor that you are unable to work full time and are on some sort of performance related pathway or reasonable adjustments have you had an independent (not a UC adviser) benefit check to see if you are receiving full benefit entitlement?
Do you have any friends or hobbies and how much motivation do you have, when you said you have done nothing today is that because you are still struggling to cope? How independent are you? Do you have any addictions that you are battling which could affect the dynamic, or will your family need to be offering support with your MH? Are your DD & SiL aware of how much support you will need? A barrage of questions but very relevant if you are moving into someone's home.
In reality just finding and organising a rental can take more than a couple of months so discuss with your DD & SiL how often you will revisit the situation to prevent this becoming unending. It can be very easy to settle into a situation and before you know it those couple of month, and more, have passed.