Do you want support because you've got two children 
or for your career generally?
Frankly, if it's the former - well, I don't think that's a reasonable reason for extra support than anyone else, whatever their personal life circumstances. We all make choices (or not) about our lives.
But, if you are asking about looking for more general support for what you describe as a career in the doldrums, then yes, that is reasonable. But frankly, your opening post sounds a bit dependent and passive. So tough love coming up.
Why do you feel your career is in the doldrums? Many of us have periods of "lower" productivity, and annoying antsy teaching. They often lead to much more productive periods where we realise that the "doldrums" were actually a period of enrichment. Can you see this period as that?
As for higher teaching loads because of covering for sick colleagues: we've all done that. Your colleagues probably did it for you on your maternity leaves. I once took no sick leave for something fairly disabling because there was no sick cover, and my colleagues were already stretched, and just last year a whole team of us had to cover for a colleague wit severe unacknowledged MH problems. It happens - it's collegiality. In an ideal world, or even a decently funded HE system, we wouldn't have to do it, but it is what it is. I don't think you can complain too much - in a permanent post, our jobs are not exactly front line zero hours factory work, are they?
In my view, you need to approach this from multiple perspectives/action plans. Your OP is about other people/institutions giving you support. If you came to me (as HoD) at the end of a maternity leave, putting it as you do, I would be tactfully & gently trying to stop you from seeing it as something other people have to do for you. I would be asking you about your existing networks: within the department, the institution & in your research area. Wat are the conferences you go to regularly, or the work you do with your rel;evant scholarly association? How could you use your networks to help you develop publications or projects? In the situation with 2 small children, networks and collaborations are going to be your way to a renewed sense of ownership & agency over your career.
I might also - depending on our personal relationship as colleagues - suggest that they years with young children cam n be a kind of "doldrums" and that we could plan together how you can do the minimum of teaching & research to keep things going, but to give you headspace. Small children take up a lot of emotional energy & that head space. But IME, colleagues come through this and get a new burst of energy when their toddlers turn into pre-schoolers, and kindergarteners. But some colleagues don't like this way of thinking ... I can see both "sides" on this. The university workplace is designed around the heterosexual married white man.
If you were really bowed down & intellectually paralysed, I might suggest a temporary period of a fractional appointment. At my place you can negotiate that for up to 5 years. Again, it's an option that not all people want to use.
I think you need to do some negotiation around modules you teach, and the RA to kick start research (that is a really jammy investment in you) - take up your colleague's feedback about a slightly reduced teaching load. But then SHUT UP about having to cover for a sick colleague. Please. Really try to think that through in terms of reasonable negotiations. At my place, we're all expected to contribute to (SL & above to run/convene) big core modules. We know that these get lower evaluations, as students always moan about core modules & we all share that pain!
However, you could point out that there needs to be a sharing of those big core modules which the department feels are necessary for its curriculum but are not popular to teach or study in.
You might also look at the research that's swilling around about the gender bias - well, let's call it what it is: sexism - in students' module evaluations. Gather your evidence, and perhaps caucus with other female colleagues to present a reasoned case about this. I always argue that on a 5 point scale, male academics should start at -3 
Perhaps present that case at a departmental meeting, where teaching allocations etc are discussed. If they are (I've always run a very democratic department where workloads, admin roles, and teaching allocations are tabled and made transparent, and I will answer to my decisions).
If there are other colleagues in your position with young children, can you meet for a writing session each month or so? I've seen this work really well: it's support from & to each other in similar situations, and works socially & intellectually.
Humanities academics don't work only as solitary researcher/writers - we need to collaborate. This is one of those situations.
It sounds as though your department/university is aware of the extra pressures on academic mothers of young children - you're lucky. And you should use this support & make it grow, by adding your own energy through collaboration & networking. It sounds as though there's good will - I think you need to take a bit of agency. That may feel difficult with a new baby, but maybe set one task every fortnight (or whatever works for you) to build/rebuild/re-energise your network and collaborations.
Think of the long game. At the moment, I expect it's hard to think past tomorrow, but can you think about the next 5 years? Where do you want to be in 2022? Concretely, that is. Then do what we all do in a big piece of research & writing: chunk it. Break it down into doable chunks.
And - I'm saying this to ALL my colleagues - DON'T overpromise! As a race, we academics tend to overpromise. we are overachieving girly swots. It's how we got to where we are. But look rationally at what you need to do - the minimum. Because the minimum is OK. Not the skiving minimum, but a high quality minimum - getting the job done well, but no more than that.