Will we ever get our house back

I would be thinking that she has moved in by stealth.

How old is she?

This sounds like good advice to me.

Together with talking openly about house hunting etc

Is building an annexe a viable option? Could you live with that as a long term solution? If so, this is a positive discussion you could have with your husband to work through the various aspects of going down this route

Agree that she needs to put her items in storage (which will cost) and this might encourage her to broaden her search criteria.
I think I would also be talking to her about finding somewhere to rent as if in a year she couldn't find anywhere I am not convinced she is really looking.

If you make her comfortable she will stay forever.
Soon you will be plotting your own exit strategy to your new flat
Start by moving her stuff to storage

I would tell your DH she needs to find somewhere to rent, otherwise it could be years till she moves or she might just decide she enjoys living with you so much and never move!

It sounds like she's essentially moved herself in with no plans to leave.

Your husband sets a time limit for her to be out to a rental if she can't find something to buy. She's had a year.

If he won't, you go from there. Would he rather be married and live with his wife and children or live with his mom? This setup is likely shit for the kids.

You need to speak directly with MIL. Ask her how the house hunting is going and is there anything you can do to help, offer to search online and go to some viewings with her etc…

She’ll get the message.

I think it's reasonable and grown up to have that conversation with your husband and MIL, especially if an annex or extension is an option.

I don't know the ages of your children but I know it's disruptive. It's fine in the short term but if it is going to a year or so, you do need to talk about options.

Obvs in a way that makes clear she's welcome and you're glad you can help her but it's not unreasonable to have some sort of timeline in place.

Approach it positively and be proactive in helping her search. Does she have a specific size/style of home in mind, a certain area, price point etc.

I'm guessing she'd be in a good place to buy and an attractive option as she's no longer in a chain and I'm assuming she's got the finances to make a downsized purchase go fairly smoothly.

Yeah no I wouldn't like that at all.

It's unfair on your children.

If she hasn't even made an offer on a property how serious is she about buying somewhere?

You need to speak to DH and set some dates for her to have either signed tenancy somewhere else or exchanged to buy

This open ended agreement will not end well

You’re not being unreasonable to find this difficult.

You are being unreasonable to expect to be given a date: nobody knows.

At the very least she could rent a storage unit.

Yes of course discuss it with your husband. Summer hols are a couple of months away and then the kids will be around more.

It's not easy to have these conversations but much better to start doing so before anyone's patience runs out.

Firstly
We are accommodating her belongings within our home,

She needs to get movers and a storage locker.

This will do 2 things.

1. Get her shit out of your home so you have more roo.
2. Focus her mind. Nit having all "her things" to hand and an actual financial impact (it's about £200 pm on storage) will encourage her to get looking.

Beyond that you need to be talking openly to her and your dh about timings and what gappens if she doesn find somewhere by X date.
You are one bad fall away from being stuck with her indefinitely....

It sounds like she needs to rent somewhere.

Buying a property can take many months! And she hasn't even found one she likes yet. You definitely need a conversation with DH, this situation is unfair on your children.
She could find somewhere to rent in the meantime.

How long has it been? Is she actively looking for accomodation?