If she is consistently £100 short a week on her bills for pretty much the past 20 years then she is doing something very wrong financially.
If she maxed out CCs all that time ago, has she just been doing minimum repayments on them?
If that is what she is doing, every penny you give her is just being thrown away to nobodys real benefit but the CC company.
It's the only thing I can think of that wouldn't eventually be paid off a bit.
Her 'pride' that she doesn't need a contribution from her 'partner' (what kind of partner would live off a single parent for 4-5 days a week without contributing when they have a job & their own home?) should not come out of your purse.
I find it highly unlikely that she is living on crisps (not actually a cheap food. A packet costs more than a packet of value noodles for instance) for food some of these days as she is so poor.
Wouldn't the partner notice & have to just have crisps himself those days? He is there most of the time.
Or wouldn't the daughter still at home see her sat there with her Wotsits or whatever (which cost more than a portion of rice when you can buy 1kg value packs so cheaply)
I personally would get everyone to sit down & explain she needs to work out her finances properly either with a debt counsellor or with family to see just where the money is going.
Without a clear understanding of why she is always so short, you won't lend her any more money.
Yes, she will find this humiliating but she should already be used to that because asking your children for money every few weeks for years because you can't manage your money is humiliating.
When my parents bitch about money (which they have no real reason to they have more than enough & a couple of mortgage free properties) I point out to them that they pay standard rate for gas & elec, they pay full price for the maximum sky package & just stay with the same overpriced car insurer, breakdown service etc... but they refuse to try & find better rates as it's too much bother so it's their own fault.
They could literally save thousands a year just by doing that.
Perhaps your mother does similar?
Nothing is going to change until you (or someone else) have a clear picture of her finances & if she won't give you that then she shouldn't be asking for money.
Something in what she is doing or spending has to change.