My youngest is 5 and I spent my day imagining how it would go with a wee one aswell (as we hope soon will happen!) and I think it would all work. The top key is to take things slow, not put too much pressure on yourself and enjoy your time with them I think. Ive always loved homeschooling so mine do, we dont sit and work to unrealistic expectations we do things in short bits, we have a very regular rythum/routine so they know what to expect and you know when you can have a cup of tea/ rest and when you can do the jobs need doing etc. The routine also means you dont feel guilty that you arent doing enough as slowly you will go through the things you hope to have them learn. It will take trial and error to find what works for your family, especially with naps etc and it will need to be flexible and gentle.
Defo dont go for the putting one in a seperate room, do things together. 5 year olds learn by play so if you have a play focused learning plan youl know they are learning and not feel things are a waste of time.
Today we did-
9.00 - 10.00 was PE -cosmic yoga & supermovers. Supermovers is amazing and thats what mine do in school, they love them and they are really learny. We also like mini disco for PE!
Then we did half an hour of worksheets & spelling practice from school. They dont like this much but they do them while I do the jobs & help when needed.
Then They did computer based learning for a bit - reading eggs, maths seeds & mystery science - these are all amazing and my eldest totally taught himself to read from reading eggs so if yours likes computer games this is brilliant. This gives me time to make lunch etc.
Then we had lunch and then went on our walk where we did puddle jumping in ice which they loved. Good chance to chat about science bits of ice!
We then stopped at the library for our books and they excitedly read them when we got in.
Then my youngest (5) did play based learning with playdo.
So kind of:
PE
Formal learning/workbooks
Computer based learning
Walk
Stories
Play based learning
So if you make a schedule that fits your day you can see what you are achieving as you go along, even though its no pressure and very free flowing.
On walks can defo do nature chats and collecting cool leaves etc for art, scavenger hunts etc. Can also play games like Ispy and animal alphabet (working together to do the alphabet with adjectives... angry ant, big bird, crazy cat etc). Quests are also fun where you use storytelling, help your eldest develop storytelling skills, use of adjectives etc by making it an adventure as you go ( today we need to find the 3 magic leaves the fairies have left out for us, watch out for tiny mice, shh dont wake the owl in that tree.... etc etc.. make it up to their interest and give them a chance to tell a tale too...)
We have great workbooks to their interest - starwars/pawpatrol/peter rabbit etc there are so many great ones you can get.
Id also say that reading stories as a three on the sofa will be really good - your littlest can see the pictures and snuggle in and your eldest can read along with you best they can? It all inspires a love of books!
And that there are soo many amazing learny TV shows that are incredible that you can all sit together on the sofa and enjoy that will be good for both ages in different ways and good for snuggle time. - Alphablocks, numberblocks etc, and totally recommend Mr Thorne on youtube for your phonics and that may be what you are needing now really, the phonics practice? He's fun for the littlest too Id think. So totally dont worry about using TV for learning, its used loads in school and is so good for learning and for snuggle family time.
You can also put the duplo/sticklebricks/bricks/ whatever on a rug to do together while you watch things.
Of course you may have buckets of formal work or zoom lessons from school and that may be different but if you can take it slow and steady (you will win that way!) make the learning fun and give the eldest a love of storytelling and learning and both of them chances to snuggle.
Millions of different play based learnings you can try. chalks (letter formation), water play (sink/float etc), jigsaws (pattern recognition) etc, things like that, its all really good.
I think its about making a plan that works for you and them where you feel some good learning is in place in a regular way that involves both children, and the more formal stuff during nap time etc and works around what needs to be done without causing stress then it will all be fine. School can tell you what to focus on? I imagine phonics and some writing practice and some number skills? Also see Twinkl is got great worksheets etc by age. Also BBC bitesize. Its all brilliant!