I am a fairly new mum but I am a behaviour management teacher for primary aged kids.
One very simple thing that might work for you as a starting point is to "set things up".
In other words don't get the kids to start playing and then tell them to be quiet. Instead set them up to play how you'd like them to.
Like" Ok lads, mum has still got a bit of work to do but it will be done quicker and we can go for a run in the park if you help. You can help by playing XXX game and this is how loud it can get (demonstrate level of noise) If you get bored with that you could also do this XXX."
If they even slightly come close to the request follow through with the suggested outing/treat.
Try about 10-20 mins of this type of thing and gradually stretch to an hour as they get better at it.
Chatting to them as you travel to home from care is a great place to do the "setting up". They are stuck listening to you. You can control outside noise (radio other people chatting) and you can reinforce any important things like " if XXX gets broken then we won't be able to go to the park 'cause we'll have to spend time fixing it".
You can also get them to tell back what you want.
I takes time to establish but it might work.
Good luck to you and you are already doing a wonderful job as you have identified what you want to fix.
Go gently
Kate