Actually it is sounding like your dh's mother is afraid of getting old, and handling it very badly. When she was in her prime she was great. Then came along a newer and prettier female version into the family, aka yourself, and she felt threatened. Your engagement meant that you were becoming a new member of the family she had to compete with on an ongoing basis, then the wedding confirmed it. Now she is in a panic and not handling it well.
The next stage of life comes along in your family and you welcome a lovely and beautiful girl, this now means she is officially a grandparent, no longer in her prime and beautiful. So she cannot function at all in this family unit where she has lost her feminine power and not wanting to confront it, as that would be naming her fear - she tells your family that she cannot be in your lives.
But your dh's father is delighted, he may not show it emotionally as most older men don't. They also don't normally know to follow up right after having children to see if all is well. Usually they wait to be told when they are needed and probably thought you'd appreciate him not being underfoot, at a big time. But he must be talking about it excitably at home, sending your mil into a panic to plan a holiday to get away from going to the hospital. He most likely thought that no big deal, again you probably would be very busy and not wanting too many visitors, so he could kill 2 birds with one stone. Keep the wife happy on a holiday, then come visit the new baby when you would most likely welcome visitors.
So they come FIL excited to see the new family member and MIL because not coming would mean having to disclose her real reasons of growing older and no longer attractive. She can't not come because in FIL's eyes that would mean she's in danger of losing respect and her feminine charm to him. So she goes along and endures, what she has to. Your FIL is obviously in love with his new granddaughter as he is talking about her to others, such is why your SIL told you that they are coming again. She knows how her mother is because she also is a threat to her beauty as a woman, and is no doubt of her mother's behaviour. So they come again. I would say that your FIL is smittened with your new baby.
It probably is time for the family to name the white elephant in the room before it gets any bigger, or just accept that your MIL cannot function well in what she believes to be a threat to her aging.