The child is in school and after school club, so the dh would not need to take 2 months off work. He would need to reduce overtime during that period though. An employer should accept this - men should not be expected to be able to opt out of all domestic responsibilities all of the time!
How long is his commute, OP? Would he be able to do the school run and still work his contracted hours?
I'm surprised at how many people think it's unreasonable to expect the DH to step up in this situation. As the main breadwinner in our household, with a very demanding job, I have never resented being on my own with dd for periods when my dh has returned to his home country, sometimes for up to 3 months at a time, partly for work and partly to deal with family issues. Single parents do this all the time, so it is surely do-able for a couple of months as a one-off. Is it because the DH is a man that people think this is unreasonable?
My biggest concern would be how the dd would cope with mum's absence, as she is obviously the primary carer. However, as I said above, I coped with similar as a child and we all survived. Then there is the question of how easily the dh could manage childcare around his job.
I totally understand you wanting to do this for your mum, OP. I hope you can find a way of making it work for you and your family.