This is such a difficult one.
Your DH's health has to be a priority, but she is also so newly bereaved and must feel overwhelmed.
My MIL relies on us too, but to be fair she is completely computer illiterate and is too old to be inclined to learn and has limited dexterity now. We do most of her admin for her. But we do it like a process, ie I put a note in my diary when her energy contracts are due for renewal, or she is due to book eye appt. etc. Then I call her a week ahead and remind her. So she feels we care enough to be on the ball about these mundane things, but know that we're expecting her to deal with it unless she asks us for specific help.
I'm not suggesting for a second that you don't care, I'm just outlining what works for us. 
DD is 12 and calls MIL twice a week for a chat about school, the neighbourhood gossip, soap/tv etc.
DD also loves to guide her other, slightly more computer literate grandparents where they can find out stuff such as bin collection days after a BH, price comparison sites etc.
As for the life admin and general reassurance, I think you need to allocate her some of your time if possible. Maybe a daily quick call as pp suggested to ask if there's anything she needs as you've got a packed day today?
We've managed to cut the admin/problem solving calls down to efficient conversations that don't then turn into random chat. It's quite businesslike, but she knows we're always here in an emergency.
Are you able to visit regularly? We visit every fortnight and facetime the alternate week purely for chat and catch up.
So she has contact with either DH, DD or myself almost daily, but there are unspoken boundaries about the purpose for each contact.
I know my MIL is lonely, and we worry about her. But I think/hope we've got a balance that works for us and her.