You've been played OP. They're both taking the piss and she's got no intentions of moving out. Don't worry about her or DH feeling she's unwelcome - she is unwelcome! Be honest about it, don't pussy foot around else you'll find your concerns dismissed as unimportant and be railroaded into accepting the situation indefinitely. This is your home and your life, stand up for yourself.
Definitely agree a date for moving out. As this date approaches she needs to be looking at rentals, she's not going to buy somewhere quickly enough. No arguments about how she "can't afford it" on her pension - she doesn't only have her income to live on, she has the sale price of the house and she's going to have to use some of it for rent. 6 months in the average private rental will focus her mind on buying somewhere!
As far as buying something goes, all this nonsense about "not being able to find somewhere" has to stop. She's not going to be able to find eg the conveniences of a 3 bedroom house type situation in a 1 bedroom flat. So she needs to accept reality, downsizing means things drastically changing and altering her lifestyle to fit her new circumstances.
She's inconveniencing you badly and your DC, she's putting a strain on your marriage and has filled your home with her crap. It's completely unreasonable. She never should have moved in. There's property for sale on Rightmove every single day. She's now at the point where she has to pick one. Rather than comparing them all to the cushy set up she has now or the situation she had before, finding the available properties lesser than and saying they're "unsuitable" as a result.
If she doesn't like where she's picked and can't settle there then she can move again in a few years, like everyone else has to do. If that happens don't accept her into your home again. If she sells without somewhere go to then she's going to have to rent while she looks.
Definitely don't build an annex! Unless you really want to be her old age carer. It's not fair your family should bare the brunt of that cost either and the alternative is her owning a stake in your property, if she pays for the annex to be built. Not a situation you want to get into, you'd be even more trapped.