OP, on that pay, I can't see any reason why she would struggle unless you are asking her to leave the HA house. I think she is trying to guilt you into staying.
You know her income so write out her budget, covering rent, council tax with 25% discount, food for the three of them, child care, utilities, and an amount for children's clothes and activities. See for yourself whether it works.
Suggest a childcare routine, that incorporates your days.
One of the biggest grumbles from mums whose partners have left, is that the
mums are left to carry the mental load of planning, budgeting etc, so help her with this part.
Maybe she just needs a bit of reassurance that she will cope fine. Then tell her a date you are leaving. Give her a bit of notice so she has time to make any arrangements.
Check what she is legally entitled to claim from you and set up a DD for that amount - not more. Then you have flexibility over what extra you choose to pay for - children's uniform, shoes, winter coats, hobbies etc. You need to eat and pay your rent as well.