The basic limitation period doesn’t run when the claimant is a minor or incapable person, except when the claimant is represented by a litigation guardian (see sections 6, 7, and 8 of the Limitations Act).
If the litigation guardian discovers that she has a conflict of interest, she must take steps to have a new litigation guardian appointed. The conflict of interest will not suspend the running of the limitation period.
Per Justice Sweeny in Socha v. Peninsula Towing & Recovery:
 The conflict of interest which is said to arise as a result of being named a defendant to a counterclaim cannot absolve a litigation guardian of his or her responsibilities to a minor. The conflict of interest may be seen as an indication that the litigation guardian has an“interest adverse” to the minor (see Murray v. Children’s Centre Thunder Bay & Murray, 2010 ONSC 845 (CanLII), at para. 25). However, the existence of a counter-claim or the potential liability of a parent has not precluded a parent from representing a minor as a next friend (the precursor to a litigation guardian) as was the case in Beckerson and Beckerson v. Dougherty, 1953 CanLII 129 (ON SC),  O.R. 303.
 In my view, a litigation guardian is not relieved of his or her duties to the minor or incapable person because he or she finds that his or her interest may be adverse. If that situation does arise, the litigation guardian should take steps to have a new litigation guardian appointed. The conflict should not have the effect of suspending the running of the limitation period.