There is evidence that pressure has been applied to the kids by their mother and her husband. If I am willing and able to have the kids spend time with me can my ex-wife file for more child support?
The Court will consider the desires of the children since they are so old (14 and 16), the real issues are (1) what do the children really feel and (2) how weight will the Court give to their respective desires. The 16 year old is old enough to file his/her own petition to change custody. You mentioned “pressure” from the mother and stepdad and that may be parental alienation but it is very hard to prove. Taking the mother to court may push the kids away further. This must feel like a no win situation so it is important to focus on strenghtening your relationship with the kids. Kids this age really want their opinions to be respected and you may push them away if you tell them how they feel and that they feel that way only because of their mother. Family therapy or just spending more time with them on their terms (shorter visits, going to movies, dinner, etc.) may get them talking about what is bothering them.
As for your child support question, if you have shared residential custody and you (or the mother) reopens the court case and a new court-ordered schedule is developed where you have less overnights with the kids then the Court probably will increase the amount of child support. I suggest speaking with a child custody lawyer about this.