Don't buy the house yet. Go and see your local housing advice centre and ask to speak to a qualified housing officer.Get an appointment.
Your stepdaughter is an adult - and if she has children under 16 (or in full time education) who she is supporting, she should not be seen to be intentionally homeless under housing legislation, and should get some help to access some temporary,acceptable! and affordable housing for rent until she has sorted out the sale of her property.
Even though she has chosen to leave her home 200 miles away, she could argue that 1)this was necessary as she has been offered and accepted work in your area by her employer 2) she needs your/your husband's practical support now she is a widow with children to be able to cope with its demands 3) this will be easier if she and you do not have the strain of sharing the same (overcrowded?) house 4)the house which she owns is now unaffordable for her now she is on her own. (Use this last argument with caution - not so easy if mortgage now paid off with life insurance) but remind the adviser it may take some time to sell.
You yourself need to say very clearly that while you and your husband were happy to help for a limited period the ongoing situation is now affecting your health (stress, depression?) and you have had to ask her to leave.If you can get a note from your doctor to support this, do so.Do NOT go 'soft' at this point in the interview. If it looks like your stepdaughter and children could be roofless, the housing department will be in a much better position to help her.
If she did not have the house to sell, she could argue she was'homeless at home' and be entitled to be housed by the council as a 'priority need' applicant because she and the children are living in your house, especially if there is overcrowding. As it is, the situation is temporary. But emphasise to them very strongly that she has no buyer, it could all take a long time to sort out, and you are at the end of your tether.She will still be able to get 'advice and assistance'. Depending on her financial circumstances, this could mean renting somewhere affordable privately (they can advise on/ensure it is a fit place for occupation) or being found some council/housing association accommodation to tide her over. She may qualify for housing benefit on either( there is a 'cap' on this).
It is quite 'reasonable' ( a legal term) for her to wish to live in the area where she has work to support her children. It is also 'reasonable' for you not to be sharing your home with her and the children for an indefinite period, so don't feel guilty.And if she is in rented accommodation this way and you have not stretched yourselves to purchase another property you may be better able to help out from time to time.
Bridging loans are expensive and if the house does not sell she/you could be in a lot of financial trouble - try this way first!
Good luck, and stick to your guns!