I don't think you should offer help financially specifically with nursery fees, because it could create resentment from you towards them if you see them spending on something "unnecessary" (in your eyes) after they've said they're broke. If you want to save up wages and give a one-off lump sum gift (even if it ends up being a series of one-off gifts) then do that, with no strings attached. Saying you'll pay for nursery fees is you attaching conditions to the money. At the end of the day you're not going to know what they see as essential versus luxury, what their definition of "broke" is and whether that holiday/new carpet/car came out of your "nursery fees" gifted money or their wages. It all ends up amounting to the same thing though - judgement and resentment - so don't go there, just gift them if you want to gift them and let them live their life however they see fit.
I'd not offer full time permanent childcare either on the grounds it isn't practical. Offer on a one-off basis (even if it ends up being a series of one-offs) if DC is sick, they want to go on holiday by themselves, other childcare has let them down etc if you want to and are able to at that moment in time. That's genuinely helpful.
Signing yourself up for full time childcare is guaranteed to create problems. Either they'll come to rely on it, taking you for granted, treating you as staff and maybe feeling resentful that it isn't all exactly how they'd like it to be. Or you'll quickly realised that 35hrs a week childcare is gruelling at your age and you can't do it. Especially when "full time" turns out to be not 35hrs you envisioned, but 48hrs standard plus commute and overtime.
It'll also hugely impact your relationship when something inevitably goes wrong. The moment you have a health issue and need their help and support will be the exact moment they're most unable to give it, because they're suddenly frantically busy scrabbling around for childcare/juggling it themselves on top of all their usual commitments.
Offering to do all school runs will get old quickly as you realise just how restricted your day is when you never get a lie in because you're collecting DC at 7.30-8am for the school drop off in rush hour traffic, don't get home after drop off until 9.30-10am, then have to leave at 1.30pm to be back at the school for 2pm just to get a decent parking spot while you wait until 3.30pm for them to come out. You're imagining a couple of peaceful, unhurried, half hour round trips at each end of the day, but it ends up taking up more time than that in reality and feels like one big rush and hassle.