"They are at least entitled to reasonable notice that they have to move,the period of notice will be in their tenancy agreement."
No - there will be nothing in the tenancy agreement about this. The mortrgage lender takes the landlord to Court & gets a repossession decision. The Court decides how long should elapse before the lender can take possession - usually a short period like 28 days. Under the law as it is now the tenant can even find the bailiffs come to evict them and they know nothing about it!
The agent has no power to check the mortgage position unless the landlord gives authority to him to do so. I think it would be most unusual for an agent to do this.
It seems to me that your daughter has been quite fortunate. Yes, she has been mucked about, but the agent has let her know the position (presumably as soon as the agent knew of it) & has offered her somewhere else & some recompense. She will have to move out, so she should accept the offer unless the place is unsuitable.
If she is doubtful whether the agent is telling the truth she could ask for details of the Court claim & decision.