Robotic systems have the potential to assist vitre-oretinal surgeons in extremely difficult surgical tasks inside the human eye. In addition to reducing hand tremor and improving tool positioning, a robotic assistant can provide assistive motion guidance using virtual fixtures, and incorporate real-time feedback from intraocular force sensing ophthalmic instruments to present tissue manipulation forces, that are otherwise physically imperceptible to the surgeon. This paper presents the design of an FBG-based, multi-function instrument that is capable of measuring mN-level forces at the instrument tip located inside the eye, and also the sclera contact location on the instrument shaft and the corresponding contact force. The given information is used to augment cooperatively controlled robot behavior with variable admittance control. This effectively creates an adaptive remote center-of-motion (RCM) constraint to minimize eye motion, but also allows the translation of the RCM location if the instrument is not near the retina. In addition, it provides force scaling for sclera force feedback. The calibration and validation of the multifunction force sensing instrument are presented, along with demonstration and performance assessment of the variable admittance robot control on an eye phantom.