what you are describing isnt covered by a distinct rule...what you have is a trainwreck..
A play at first base often makes it possible for the throw to take the fielder into the same space that the batter runner needs to touch the base...when both the fielder and the runner are doing totally legal things and contact is made, its commonly described as a trainwreck....
As to how long a fielder has to hold it, well that is covered under the definition of a catch...
A CATCH is the act of a fielder in getting secure possession in his hand or glove of
a ball in flight and firmly holding it; providing he does not use his cap, protector, pocket or
any other part of his uniform in getting possession. It is not a catch, however, if
simultaneously or immediately following his contact with the ball, he collides with a player,
or with a wall, or if he falls down, and as a result of such collision or falling, drops the ball.
It is not a catch if a fielder touches a fly ball which then hits a member of the offensive team
or an umpire and then is caught by another defensive player. If the fielder has made the
catch and drops the ball while in the act of making a throw following the catch, the ball shall
be adjudged to have been caught.
In establishing the validity of the catch, the fielder shall hold the ball long enough to prove that he has complete control of the ball and that his release of the ball is voluntary and intentional.
