If you're already finding it challenging doing 4 days, it would be incredibly stressful trying to do the same job in 3 days. You'd always find yourself playing catch up, and possibly be giving yourself to work on the days you'd be working. Plus it would probably be viewed negatively by your colleagues. I'd stick with the 4 days at work in you can, then you do childcare the other day.
It's not clear how much childcare across 4 days your DH and mum would be doing, so I'd sit them both down and work it out between you.
In our case, my parents looked after both our DCs (only 12 months between them) full-time from the age of 7 months to 1 year, then they went to a wonderful nursery 4 days a week, which opened 7.30am-6.30pm. Pre-Covid, DH and I flexed our schedules so that one of us would drop at 8am, and one would collect at 5pm. The DC absolutely love the nursery, and have thrived there.
It really helped that my parents made themselves available to pick up the slack if we had late running meetings, or any sickness cover. We were lucky that we've only been called to nursery for sickness 2 or 3 times across the gross 4 years DC have been attending, however they had chicken pox one after the other last year, so my parents looked after one or other of them at home for a straight month.
I'd say it may help maintain a good relationship if you try not to rely on your mum too much and be conscious that she's getting older, and may also have her own appointments etc to attend, plus she'll need time for herself. Perhaps think about a childcare schedule of 2 days nursery, 1 day DH, 1 day mum, 1 day you.
I'm not sure of your domestic arrangements, but we outsource lots, cleaning, gardening, window cleaning. We used to buy-in DIY help as well, until I discovered a knack for it, so now I do that myself.
I'm not sure on the differential in price between Nanny and nursery (as we have 2 DC there and only 15 free hours, nursery is double our mortgage), however what's good about nursery is they are open 50 weeks of the year, and we don't need to think about how to cover their holidays/sickness.