I can't imagine this being doable full time, but part time over 2 years would be manageable.
I am 49 and halfway through a 2y distance MA in a subject related to work. It is HARD. My situation is not the same as yours so just to clarify:
I work 4 days a week
2DC 11 and 13, eldest has ASD but both need parenting in many ways: emotional support, monitoring phone use, homework, having friends over, 5 activities between them
DH works ft but has only just returned to work after having resigned from his last job and being off with depression. Doing OK but I am supporting him of course and cannot lean on him hugely, although he does a lot of lifts and fair share of housework
DH and I both have elderly parents who need support so one of us is away 2 out of 3 weekends
Energy wise, I am not 100%, possibly perimenopause and also stress due to the problems with my parents and DH over the last year.
Points I would consider:
My MA is supposed to take around 15 hours a week. I thought as a fast reader I could do it in less, but I cannot. It is intended to be rigorous and it is. I did a masters 20 years ago and don't remember struggling, but that was pre kids when my mind was much fresher!
Be realistic about how much you can do . If I've been up since 7, busy with kids and work the whole day, and by the time chores are done, it's 8/9 and I am tired, can do a couple of hours maybe but I do need some downtime. That's just me though - your energy levels may be better. And sometimes my kids are rattling around and want to talk to me at this time. I get little uninterrupted time.
In a normal week, I can manage. However, plenty of things interfere with this, eg school holiday, illness, group projects, family birthday / other weekend plans - you get the picture. Even with turning down plans, it's a struggle. Before coursework deadlines, it takes a lot longer. I have used annual leave to study. I do get 6 weeks annual leave from work then another week as study leave. Even so, I have only managed a one-week holiday this year.
So I would say you need some flex in the system. It sounds like your life isn't that busy apart from work and your kids are not demanding, so it sounds like part time would be ideal and you'd have no problem doing it in that time.
I should say I really enjoy the study, which is important as you need to drive to keep going!