I'll admit I find this interesting. thebird you mention things you'd like her to do for you as well as mentioning that you don't hear from her for weeks. I'm baffled.
First of all, are you or your DH "phone-challenged" and unable to use a telephone? Neither of you call her regularly to check and see how she is doing, just to say hello? Make sure she is alright and well? We speak to my MIL at least 3 times per week, often more, just on the phone, not including visits. She lives about 10-15 minutes drive away from us. Between us, our adult daughter, and our adult son (and our DIL), MIL gets calls from us probably once a day just to chat and say hello and see if she needs anything or wants company or whatever. We didn't call quite this frequently before FIL passed away 2 years ago, but still spoke to her at least twice a week and visited at least once a week before she was on her own.
We also pop over to visit on a regular basis, even if it's just a short visit with the children, so we can spend some time with her and she can see the grandchildren. I pop over sometimes and have a chat and some tea with her, and we always make sure that when the weather is bad or roads are icy that we visit and see if she needs anything picked up so she doesn't have to drive in the rough weather. We also help out with little jobs around the house and invite her to ours for meals or coffee, as well as going out for meals occasionally. When we went to visit DS1 and his family (couple hours away), we invited MIL along as it's a long drive (which she can do, but if we're already going and there's room in the car, why not invite her along to enjoy the trip?) so she could enjoy a big family visit.
We have asked MIL to assist in watching our little ones (we have a 4yo and 1yo still at home) on a rare occasion (emergency hospital appointment and also when I was in labour with our 1yo), but 4yo is SNs and quite a bit to take on, so we're not comfortable leaving both children with her (to be fair, we're not comfortable leaving both children with anyone - they're hard work!
). She's offered, but we don't want her to feel like we're just keeping in touch for babysitting.
But the communication and assistance goes two ways, surely. You seem to expect her to help you out and ring you, but you don't seem (from what you're saying) to be doing the same for her, which is a bit appalling when you consider she is an elderly woman on her own, whereas you are younger and have a partner to help you.