Not all relatives are nice and kind sadly nor emotionally healthy or safe to be at all around.
People like your MIL will fall out with nice people over anything they perceived to be as a slight against them. Its not your fault she is this disordered of thinking and you did not make her that way, her own family did that to her. Also your DH has known her a lot longer than you have and he says she is being petty and using this an excuse.
And no, do not take this on the chin for the sake of your children. She never thought of or saw all that much of them in the first place and you state yourself she is not nice. By not contacting you she has actually done you people a huge favour.
Children are often quite indiscriminate in their love which is why they need parents to guide them. Not every person is safe to have around and this is a good time to teach that important life lesson. The more matter-of-fact you are, the more matter-of-fact your children will be. When we act hysterical, they will usually reflect our hysteria. If you act anxious, they will act anxious. If you appear unsure, they will push. Model the reaction and attitude you want your children to adopt.
Young children are not known for their long attention spans. This works in your favour. With younger children you have the advantage of distraction. It is easy enough to get the child's mind off onto another track. Every parent has done the distraction routine at one time or another. "Mommy, I want to see NastyGram today!" "Honey, we aren't going to see NastyGram today because we get to go to the park and eat ice cream." (Make up fun time on the spot if necessary for this distraction.) "Yay!!" says the kid and off we go. Subject changed, kid distracted. In time, NastyGram will fade from memory. Any bonding that may have occurred will dissipate in the process of time.
Remember, you are the parent. You're older and therefore more experienced which is the point of being the parent. The child is dependent on your good sense and protective wisdom. You're smarter than your child; use that to your advantage (such as using the distraction method). You are the final authority. This is not a negotiable issue. Your child doesn't get to decide on this one because they lack the understanding, wisdom, experience and good sense that, hopefully, you have. So don't look like you're unsure or open to quibble. You'll undermine yourself if you look anything but firm and resolved on it. Use your advantages as parent to smooth the effects of the cut-off. Over time this will all quiet down. Kids tend to accept what is. It will happen more quickly if you follow the above advice.
Most of all, do not operate from a fearful mindset. Don't be afraid of your children's possible, or actual, reactions.