Questions:
* It is not clear which device is supposed to control T2. Your on/off button (near R1) can turn on T1, and that turns on T2. However the controller (shown as V2) also turns T2 on-off. It appears as though the two can compete with each other. Or did you intend for one to override the other?
* I'm looking at T4, which appears to be oriented so that current goes into the source terminal. If the FDN306P is like other mosfets, then it has its terminals designated 'source' and 'drain'. The drain should get the more positive polarity of juice. It may contain an internal diode that permits current to flow the opposite way, though not under control by the gate. By putting T4 'back to back' with T3, you may find it is workable according to the simulation. However real mosfets may be damaged by reverse current.