A four month old could begin to take a cup or a sippy cup.
This baby is probably not going to make this change without resistance.
Smart baby, we always say, ok ok. . .  But when there is no other way,
gentle loving flexible persistence will work eventually.
Try sitting the baby in the car seat or similar.  It goes against one's
grain not to hold a baby during feeding, but it worked for me and the
little three month old I began babysitting over a year ago. I gave EBM
in a sippy cup, because she would not take a bottle and I could tip
enough in to wet the tongue and she would smack her lips and we could
talk and smile.  Lots of animated attention is a good distraction.  Of
course, I began the feeding before she was very hungry. Every now and
then I would see if she would suck on a bottle.  She developed an
uncanny way of being able to suck all the air out of the bottle,
collapsing the nipple, without taking more than half to an ounce at most
of EBM in about 45 minutes.
I remember a method of bottle feeding that Diane Weissinger (I hope I
got the name right) told me about some years ago on Lactnet.  This
method allows the baby more control over how fast the bottle feeding and
how much the baby takes. This baby seemed to know naturally how to take
the bottle inn a similar way.  It was interesting.
After three sessions giving her a cup or bottle in the car seat, she
began to let me hold her.  She was very active, though--lots of
squirming that I learned to roll with.  I suggest moms or caregivers try
other ways of holding the baby--maybe you have suggested she try them,
too.
Suggest mom talk with caregiver so that there is understanding all
around.  If mom has enough confidence in the caregiver she can leave the
whole shebang to her two weeks from now and just enjoy the time she has
left at home without having to struggle over teaching a new feeding
method.
Helping my little friend to learn a new feeding method (and learn to be
away from her mom--hard to know which was more difficult or if it was
both: yes) was a very emotionally draining experience for me, even if it
did last only three days.  I almost didn't make it, meaning I was on the
verge of telling the mom that she couldn't leave her baby, but brought
ear plugs to my babysitting gig instead (I didn't need to use them).  I
do want to say that I held the little one throughout her anguish (and my
ears, and my heart).

Diane, LLLL from VT