Zaza, stress, tiredness and guilt sound familiar, though I am a lot more selfish. After a crisis, it takes months for stress and tiredness to ease. All I can suggest is that guilt, in any form, is a waste of emotional energy.
Then triage. You have things you need to do, and then things you also need to do, which includes quality time with your teens, and some time to yourself.
The latter might include an afternoon spent watching tennis, Tour de France or whatever, not getting out of bed on a Sunday morning and having your kids bring you breakfast, binge watching or reading something easy (my own solution of Netflix and an iPad, which I got for recuperating from an operation, proved perfect for A levels and the nights DD could not sleep. We would simply lie in bed watching an old episode of a favourite programme, till she was sufficiently distracted to feel sleepy), gardening, baking, spa session, walking (I have joined a walking group), or a drink with a friend who will listen and let you off-load. You are also important. And looking after yourself is a priority.
Yes, your mother is lonely, and you should ensure you spend some time with her, but she is not always the over-riding priority.
Is there scope to do more than one thing at once. DD needed to do some volunteering prior to her University applications, so spent the summer working at my mother's sheltered housing. We also managed to include her in a beach BBQ this week, which went well. She was comfortable sitting and watching, and seemed to enjoy being part of a group.
We would all like our parents to be happy. But old age is miserable, and to a large extent how people cope depends on the networks, interests and coping skills they have built up over their lives. We can't do much to change anything, and also have duties to our children and ourselves.