Well, if your SIL is so darn educated you can hit her with some of these references...
In the second year (12-23 months), 448 mL of breastmilk provides:
29% of energy requirements
43% of protein requirements
36% of calcium requirements
75% of vitamin A requirements
76% of folate requirements
94% of vitamin B12 requirements
60% of vitamin C requirements
[Dewey KG. Nutrition, Growth, and Complementary Feeding of the Breastfed Infant. Pediatric Clinics of North America. February 2001;48(1).]
Children weaned before two years of age are at increased risk of illness (as per the American Academy of Family Physicians, although I can't find a specific reference).
Nursing toddlers between the ages of 16 and 30 months have been found to have fewer illnesses and illnesses of shorter duration than their non-nursing peers.
[Gulick EE. The effects of breastfeeding on toddler health. Pediatr Nurs. 1986 Jan-Feb;12(1):51-4.]
Antibodies are abundant in human milk throughout lactation. In fact, some of the immune factors in breastmilk increase in concentration during the second year.
[Goldman AS, Goldblum RM, Garza C. Immunologic components in human milk during the second year of lactation. Acta Paediatr Scand. 1983 May;72(3):461-2.]
Apart from protecting the mother against breast cancer, increased time spent bf also offers some protection against ovarian cancer:
Gwinn ML, Lee NC, Rhodes PH, Layde PM, Rubin GL. Pregnancy, breastfeeding and oral contraceptives and the risk of epithelial ovarian cancer. J Clin Epidemiol 1990;43:559-68.
Hartge P, Schiffman MH, Hoover R, McGowan L, Lesher L, Norris HJ. A case control study of epithelial ovarian cancer. Am J Obstet Gynecol 1989;161:10-6.
Rosenblatt KA, Thomas DB, and the WHO collaborative study of neoplasia and steroid contraceptives. Lactation and the risk of epithelial ovarian cancer. International J Epidemiol 1993;22:192-7.
Schneider AP. Risk factor for ovarian cancer. N Engl J Med. 1987 Aug 20;317(8):508-9.
and uterine cancer:
Brock KE et al. Sexual, reproductive and contraceptive risk factors for carcinoma-in-situ of the uterine cervix in Sydney. Med J Aust. 1989 Feb 6;150(3):125-30.
and endometrial cancer:
Rosenblatt KA, Thomas DB, and the WHO collaborative study of neoplasia and steroid contraceptives. Prolonged Lactation and endometrial cancer. Int J Epidemiol 1995;24:499-503. [I think this may only apply to lactational amenorrhea, though, although I'm not sure]
and osteoporosis:
Blaauw, R. et al. Risk factors for development of osteoporosis in a South African population. SAMJ 1994; 84:328-32.
and rheumatoid arthritis:
Karlson EW, Mandl LA, Hankinson SE, Grodstein F. Do breast-feeding and other reproductive factors influence future risk of rheumatoid arthritis? Results from the Nurses' Health Study. Arthritis Rheum. 2004 Nov;50(11):3458-67.
Perfectly possible to nurse through pregnancy and tandem nurse afterwards with no ill-effects for the new baby. After all, you're designed to be able to nurse twins round the clock, so a toddler having a couple of feeds isn't going to impact your supply for the newborn. Some toddlers do self-wean while the mother is pregnant, though.