In such case file an IA R/w S. 151 CPC with prayer ot dispose it either way before other matters comes before the concerned Court by stating few names along with admission deadline dates / forms of such schools from your side with assurance to Court to bear complete educational expenses voluntarily showing better all round development of a child and a father's concern who is seeking custody of his child.
Now here what will happen is that wife will come with two facts; one that she will bring her own list of schools or two she will simply say that the child is already admitted in a school and doing fine!
Now that is the catch here, it will now be your turn to argue vehemently then and there to put child in the school which you find better and state all the better reasons and also give assurance to Court that given shortest time I will ensure child admission in the school which I and pleading before you for the child to be admitted !.
By saying so the court will be further put in a square box situation in terms of allowing remedy or giving its own reason to dissallow so and to wriggle out from box like situation now Court will say sorry the child is already in a school so now what you want?. At that moment seek all sorts of PTM to extra curricular activities visits to schools, home work assistance each day 1 hr. and meeting with class teacher / principal etc. rights will suffice show causing your concern for keeping tab of child education and supplement it with voluntarily bearing school educational fees directly with the school on and or before the due date with copy of tuition fees met given to mother of the child.
in a situation where mother brings her own list or lack of any to court on your IA it will be your best speech on merits of a particular school with edu. Expenses + PTM etc. that I wrote above will make way for you to come up with some magic and get the child admitted in a school of your choice. But all these should be genuine concern not one gunmanship frivolity mind it just to settle some score with custodial parent which Court will find out during forced argument son your this IA (Interlocutory Application).
Your main purpose of seeing child getting education as well as you bearing edu. expenses will be solved in one shot (if already not got as some relief via some other IA) and Court will also feel back of its mind that father has real concern and simultaneously diffuse either of the above two biased 'cause of action' situation that impromptu arise in custody matters and equally well countered by both parents.
Ultimately what happens here is that a child is admitted in a school at right age plus a non-custodial father is able to meet his child at school on due dates plus he is in control over edu. expenses of the child which has colly. bearing as detailed in S. 17 of GWA – welfare of child to your custody suit.
Also always follow below illustration in any nature of judicial situations;