What a sad situation. She wants desperately to be a part of your family’s life, but her approach to it is putting distance between you. I understand completely why you want to avoid a confrontation, but that doesn’t seem to be helping, does it? Your mom probably thinks she is only being helpful. She doesn’t seem to understand that it is your right to run your house and to care for your kids as you see fit.
The only thing I can think of is to involve a mediator, i.e., a third party who can keep things civil while you try to work things out. If you have a relative who is practical and good at problem-solving, you might ask that person to help you manage a discussion with mom. If you don’t have such a person in your life, do consider asking a family therapist to help you by facilitating such a talk.
If your mother won’t agree to that, all you can do is keep her visits short — preferably at her house. That way, you can gather up the kids and leave if she becomes insufferable. There is no point to fighting with her since she seems impervious to your objections. Simply calmly state that since she won’t respect your limits, you must leave — but that you can all try again some time soon. Drawing boundaries calmly and clearly is generally more effective than debating or arguing. If she sulks, she sulks.
You needn’t feel guilty for lovingly drawing some boundaries around her behavior when she is with you and your children. Chances are that once she sees that you will either leave or ask her to go when she crosses those boundaries, she’ll modify her behavior. She does seem to want to have a relationship. Apparently she doesn’t know what to do if she isn’t the boss.
I wish you well.