ControlSend would be optimal but most poker clients do not use the standard windows controls.
You have to do something like below. Store the mouse position, do the click, return mouse pointer back. id is where I've earlier stored the id of the client window. The WinActivate is not needed if your client window is active already.
BTW you could run into problems (clicking the wrong place) using the direct coordinates if you resize your window...
MouseGetPos ,mx,my,id
CoordMode ,mouse, relative
WinActivate , ahk_id %id%
WinWaitActive, ahk_id %id%
BlockInput, mousemove
click ,%clickx%,%clicky%
CoordMode ,mouse, Screen
MouseMove mx,my,0
BlockInput, mousemoveoff