You'd lose some council tax credit too, it would drop by 50% because she'd be considered liable for half of the council tax. You'd lose the 25% discount for being the only adult in the house if mum's living there. So that's 50% of the total without discounts, that she'd have to pay.
If you're currently entitled to the maximum council tax credit and that covers the entirety of your council tax bill, your 50% would still be covered by your council tax credit. If your council tax credit amount currently covers only 90% of the council tax, it would cover 90% of that 50% that you're liable to pay.
This is because your mum isn't going to be there for a few weeks. That just isn't going to happen. She's going to move in effectively permanently. Then take months to find a job and a landlord that'll accept her as a tenant, if those things happen at all.
She's already being picky. Doesn't want to live in a refuge and refers to working as "getting a little job", showing she's got no idea whatsoever of the hoops you have to jump through to get a job or secure a rental. This isn't the 1980's, which is how she's talking. So you'll find that once she's got her feet under the table at your place, she's not applying for anything and everything, either with jobs or housing. Because getting a job and moving out won't be her top priority, finding something she likes will. And that's totally unrealistic.
With her attitude, you'll find she's barely applying for anything work wise, giving poor applications and interviews and saying things like she can't afford to move out - because she can't afford the type of property she'd like to live in, in the area she'd like to live. You'll be back on here in a year's time bemoaning the situation and looking for tips to get her out without actually kicking her out, because she's your mum and you can't bear to do that. Which means you won't be able to get her out.
If she asks about council housing she has to make it clear she's fleeing domestic abuse and is therefore homeless. NOT saying stuff like she can live with you temporarily. The minute they hear that, they'll wash their hands of her. If she's going to apply as homeless she's got to accept she's going to end up in temporary accommodation, which she'll have no choice over what it is and might mean a refuge (and that would be a darned sight better than a hostel) or a B&B, until she's successful bidding on a one bedroom HA flat (which is all they'll give her).
Honestly, I don't think she's got any realistic plans other than playing on your heart strings and moving in with you permanently, at your expense.