My first thought is how easy must your job be if you are confident you can look after a baby at the same time. Unthinkable in my job and I imagine in most people's. It must mean that your role is basically semi-redundant.
This.
Juxtaposed with this:
I work from home for the DWP and I have 3 children at home.
What some posters are missing, in their keenness to urge the OP to complain about discrimination and unfairness, is that public sector bodies don’t have shareholders and aren’t required to make a profit: all they do, pretty much, is spend and as an ex-senior civil servant and chartered accountant, I can tell you that the public sector really isn’t held to account as it should be.
It is telling that the posters boasting about their enlightened managers allowing them to care for babies and ‘work’ at the same time all appear to be employed by the public sector and are the most vocal in encouraging the OP to kick off and demand advantages for herself. Those that aren’t encouraging her to lie, of course.
Can you see that meanwhile, in the real world, businesses have to make money to survive and can’t carry the cost of economically inactive staff members? The work still needs to be done, suppliers still need to be paid, there’s a salary bill to meet each month, VAT liabilities have to be met.
The OP’s employer, which happens to be a local authority, has offered a reasonable compromise: part time working. The OP doesn’t want to take it because it doesn’t suit her, financially.
I say well done the OP’s line manager for behaving responsibly and not, like the line managers of some posters contributing to this thread, saying, “oh, it doesn’t matter if you are hardly doing any work, come back full time and look after the baby at home whilst nominally working”. Consider whether the people making this concession are hoping to benefit from it themselves in the future. That might be more important to them than exhibiting fiscal responsibility with other people’s money: yours and mine, in the form of tax revenues.