I wouldn’t bother trying to cover year 2. Likelihood is you’d bore dc to tears and lose cooperation!
First I’d join Twinkl (first 30 days are free) and I’d download a curriculum map for Year2 and read carefully to be familiar with content. The id download a couple of the KS1 SAT-style assessments for English and Maths and spelling. See if dc can mostly do this independently; if anything is tricky then download some individual worksheets and focus on those for a week.
Then repeat for y3. Twinkl has a mountain of revision material you can download and make sure you have no gaps in English, maths.
Don’t forget that you also need to think about SpaG (spelling and grammar), handwriting, times tables.
I would also download a couple of “spelling mats” for KS1 and I would check dc has nailed all the spelling for year 3 also.
By end of year 3 they should thoroughly know 2, 3, 4, 5, 8, 10. A lot of schools use use TT rockstars and my kids had nailed these tables by end of year 2. Note they should be as good at division as multiplication (instant recall), whilst perfection isn’t required until end y6 having the facts at their fingertips reduces cognitive load in lessons so they can focus on learning other things.
By end of year 2, at my kids’ state school everyone is doing very nice, even joined-up handwriting in pencil (no pens yet) using regular lined paper, but still writing quite slowly and we are expecting a lot of spelling errors! They should be using initial capitals and full stops, and starting to add adjectives and adverbs. By end y3 they can write faster and with fewer errors and obviously a range of increased sophistication. Some kids get their “pen licence” during year 3 but definitely not all of them; writing with a pencil is still ok.