Before we get to the big question, you make a good point that one solution, if the mother were willing, would be for her to pump and provide you with enough breast milk to get you through the night. Contrary to your wife’s claims there are no cases guaranteeing a privacy right in the Constitution, but it is unlikely that a Court would order her to pump since an order would be difficult to enforce.
You would probably have to use formula.
In any case, it sounds like Mother would not agree to this solution. She may argue that she cannot pump enough or that pumping might affect milk supply or lead to “nipple confusion.”  In the face of these objections, you would have to consult a pediatrician. If pumping is not the solution, it leaves unresolved the bigger question which is whether the “breast is best” argument trumps all others. While breastfeeding is important does it outweigh the benefits of father-child bonding and, if so, for how long? There is a wealth of developmental literature that shows that it is in the best interests of the child to have early father-child bonding and sooner or later bonding requires overnight custody.
The problem in your case is that the data doesn’t really address this balancing of interests and needs. The American Academy of Pediatricians in a revised 2005 policy statements states: “Exclusive breastfeeding is ideal nutrition and sufficient to support optimal growth and development for approximately the first 6 months after birth. Infants weaned before 12 months of age should not receive cow's milk feedings but should receive iron-fortified infant formula. Gradual introduction of iron-enriched solid foods in the second half of the first year should compliment the breast milk diet. It is recommended that breastfeeding continue for at least 12 months, and thereafter for as long as mutually desired.”
So you might argue that by 18 months the benefits of breastfeeding are outweighed by other factors such as father-son bonding. This conflict also needs to be viewed in a wider context. Public recognition of the health benefits of breastfeeding is a relatively new phenomenon. According to U.S Census Bureau data in the 1970’s only 10 percent of mother’s continued to breastfeed their children for six months and from 1990-1993 this figure had only risen to 28.4 percent. It is highly likely that the lawyers and judges handling your case were themselves formula fed with no long term harmful consequences. It would seem that on balance you have a good argument for seeking overnights although much depends on many other factors. You should in particular determine whether the Courts in your area have issued any parenting plan guidelines in your jurisdiction.
For example, Los Angeles County Superior Court has issued tips for creating a parenting plan that do not recommend overnights for non-custodial parents for babies up to 6 months. Instead they recommend three non consecutive days per week for up to two hours each day. For infants, 7 to18 months of age overnights are only recommended, if appropriate. Again it may be necessary to retain the services of an expert or to request that the court order a child custody evaluation if you still cannot agree. You might even consider serving a subpoena on your son’s pediatrician to see what his or her opinions are. Other considerations which you should explore are whether the mother has exclusively breastfeed other children for such a long period of time and, if she works, does she exclusively breastfeed at work. For an excellent discussion of baby development see “How the Brain and Mind Develop in the First Five Years of Life” written by Lisa Eliot, Ph.D (Bantam Books, 2000).
 See Shana M. Christtrup, “Breastfeeding in the American Workplace” Journal of Gender, Social Policy and the Law [Vol 9:3] at http://www.wcl.american.edu/journal/genderlaw/09/9-3christrup.pdf?rd=1
 Studies show that “nipple confusion” – difficulty switching from one form or feeding to another -- is most prominent when an infant is about three months old.Warren R. Shiell has practiced law for more than 15 years in the United Kingdom, New York and California. His firm in Beverly Hills, Calif., is devoted exclusively to family law issues. His web site is http://la-familylaw.com/.