This is going to be a bit more general, as my situation now is so different from yours. But if you are going to have the "old folks" like me on here, you might as well learn from our mistakes, eh?
New baby - you are a "family" now (not that you weren't before, but now it should be obvious to your parents). Your visits will/should change, accept that fact. Most importantly, the "major" holiday visits will change (for Canadians that is usually Christmas, for Americans I get the impression it is more Thanksgiving). And of course everyone wants to see the baby. But your travel priorities and family priorities have to be set now, or soon, or you will be hauling kids all over the place to keep family happy, and you will not necessarily be happy. I speak from experience, we did it wrong. We had a 3 hour drive to one set of parents, then a three hour drive to the other set of parents, then a 3 hour drive home - and every year we did that over Christmas, when the roads can be bad (one year we drove in what was almost a blizzard, nerve-wracking). Because we didn't stand firm. And we kept doing it after DD came, so our family Christmas tradition was set up the tree, enjoy pre-Christmas at home, and then get in the car and drive. Not the best memories for DD. Or us. I have always felt that we would have been a stronger family if we had put our little nuclear family ahead of both sets of parents. And yes, I am now divorced. How much did that contribute, who can say? But I sure felt that I was lower priority than his parents. They were the ones who pushed for us to come, mine were much more "come when you can, no issues". Who has higher priority for each of you, your parents or your spouse? I was at a wedding once where the priest pointed out that the "others" in "forsaking all others" includes your parents, so now your spouse comes ahead of your parents - I thought that was a good message for the parents to hear.
Travel points (for when you do go) and Skype will save you. A friend of mine bought a tablet for her mother (who is an ocean away), her daughter visited and got it all set up, and now they all Skype all the time and everyone is much happier. Plus the daughter is meeting cousins over Skype that she had never met when she visited, since they can also pop onto Skype.
Side comment - all this visiting is because travel is relatively inexpensive. Everyone here (except Native Americans) comes from a family that immigrated and probably never expected to have contact with the "old country" except by mail.