I have to agree with natjojo. We live 2 doors down from my ILs and it's a godsend. Free childcare and a lovely sense of a close knit family. I am very blessed with a really lovely MIL and FIL (my MILs mum also lives with them) Of course things aren't always perfect. Sometimes we have minor disagreements and feel a bit tense towards each other, but that would happen in any relationship regardless of distance.
My kids have a really amazing relationship with their grandparents and great-nanny. It's really lovely to see. My 3 year old makes a beeline for her great-nanny all the time and will want to call over and read books with her a lot. It makes her day. I hope when I'm 86 I have a grand-daughter or great grand-daughter that does the same.
We lived right next door to my step-GPs growing up. My little sister particularly benefited from this, as when her and mum went through a really rough patch when she was a teenager, my sister would storm off up to her nanny. Not ideal, maybe, but a lot better than her storming off to go drinking in a park or something like that.
I think separate house are much easier to handle than actually living together. Maybe it's worth thinking about what it is that you think would change with her living next door vs her living very close by, where she is now, and discussing this with your husband?
Maybe once you've worked out what it is you are specifically worried about you can address it, and come up with some solutions. Do you think your kids would like having their nanny next door? Maybe your kids calling in with her will alleviate her loneliness and she won't actually be round at your house much? Can you see any other pros apart from the wood burner and garage? Maybe you'd feel more comfortable with some ground rules set down around her dropping by unexpected.
Saying all that I don't know your MIL, So I don't want to push you along on something that you think will honestly be unbearable.