Three year olds can certainly use cups--fluids other than breastfeeding should
be given by cup for any child over 12 months of age.
Cow milk can be quite constipating for some children.  The mom should try
eliminating or reducing the cow milk for a few weeks to see if the
constipation clears up.  She should remember to watch cheese intake, also.
The child may well be stool holding intentionally.  This is quite common in
children of toilet-training age.  Mom needs to devise a behavior-mod technique
for encouraging regular stooling (stickers on a calendar in the bathroom, with
rewards for daily stooling would work--and rewards could be an extra bedtime
story, etc., not an object).  Mineral oil can be given to ensure soft BMs.
Sounds like the child isn't ready to wean from the breast, either, and may be
stool holding in protest.
My suggestions:  1)  Get rid of all baby bottles.  2)  Reduce or eliminate cow
milk.  3)  Try a behavior mod system for regular stooling.  4)  Wait for
awhile to wean from the breast.
Linda L. Shaw MD FAAP