to op: Mazel Tov on your marriage may you be Zoche to build a Bayis Neeaman Biyisrael!
Try having your mother do an activity together with your wife.Maybe your mother could take her or the two of you out for pre-pesach dinner does not even have to be fancy, or invite over to the house,in the middle of conversation see if some common interests build up,i.e. your mother and wife both like such and such book,speaker,restaraunt or a certain museum and then your mother could build from there.
Another thing is if your wife mentions she needs something before yom tov your mother(as long as she will not be interfering) can tag along with you and your wife for the shopping and do the groceries or other tasks together. If it is clothes shopping your mother can solicit your wifes advice about an article of clothing for purchase. This will show your wife that your mother values her opinion and other shopping expeditions and social interactions may follow.
Spending part of yom-tov with your parents will be able to foster a closer relationship in a very positive and natural manner.As this is your first Pesach together, you should emphasize to your wife how happy your parents are to be having her for yom tov, and have your mother compliment her.There so many easy conversations that can be had over Yom Tov especially Pesach, such as recipes afikoman presents, chol hamoed trips minhagim etc….Let your mother just let the conversation flow naturally. I am sure that their bond will be stronger after Pesach.
Re your wife: Boruch Hashem I am sure you married a wonderful person with excellent middos,this is an issue that will go away by itself naturally.Bezras Hashem you will soon see the wonderful relationship your mother and wife will develop.