Hi, Adult Social worker here. Definitely my field. She doesnt appear to me from your scenario, as if she would meet criteria for Mental Health Act assessment.
But you do need to speak more to her CPN (Community psychiatric nurse). If she doesnt have one, ask her GP to refer her to the local CMHT (Community Mental Health Team). You are essentially concerned about her deteriorating short term memory loss & capacity, she appears to be becoming disorientated in place, at risk of wandering, her risks are increasing and DP's sis is under main carer strain. Get her CPN involved and on board. It will help you.
It depends on what DP's sister wants. Does she feel she's at the end of the road now, she cannot manage anymore and her mum needs to go into residential care? It really is her call as MIL is living in her house.
If you are all in agreement, then you need to ask social workers back to reassess her needs, explain her needs have changed.
Ask them to assess her mental capacity under the Mental Capacity Act (MCA) 2005, on whether she understands her level of care needs and can make a decision about whether to move into a care home. The CPN could also assess her capacity in this area and tell the social worker (only one professional needs to assess capacity).
If she is assessed as not having capacity to make that decision, then her family, the social worker, her CPN, doctor/whoever else is involved will all make a Best Interests Decision for her, which might be that she needs to move into residential care.
You need to be sure that the social worker has full list of risks and risk incidents that have happened so far including when (date/time) and number of times she has tried to wander. What care is provided to her. How much prompting and orientating she requires to do her daily tasks.
The Best Interests Decision depends on each individuals risks, what everyone knows about the person's past and present wishes, any advance directives and what the least restrictive options are (that adequately meet her needs).
For example there are alternatives to residential care, including extra care sheltered schemes. There are also lots of respite options to give DP's sister a regular break if she is not keen herself on MIL moving permenantly into residential care. As well as residential care being an option.
The MCA does not give you powers to convey someone to the home if they refuse to get in the car, but talk to the social worker/CPN as they will be full of advice.
Getting LPA for finances and health and welfare is a great idea and good future planning. However if the solicitor agrees that she is still able to give you LPA (Lasting Power of Attorney) at this point via a solicitor, then s/he is advising you that she has testimonary capacity (the solicitor makes this call) at that point.
In which case, this might indicate to me that she possibly may retain capacity in other major areas too (but they are separate tests for each decision so this is not a given).
I hope this helps.