You might make it in 3.5 hours but it will be kind of a miracle.
It takes at least 15 minutes for your flight to taxi to the gate at LAX so if your arrival time is 3:45 pm, you probably won't deplane until at least 4 pm, possibly much later. And you mention you will have luggage so that's another 20~25 minutes before you can leave T3. So it is almost 4:30 pm by the time you reach the rental car shuttle waiting area.
Friday afternoon is going to be hellish at LAX. It will take about 30 minutes to navigate the loop and back to the rental car lot. Since you are Hertz Gold, you can probably just jump in any car and go. Otherwise, there is another long line on Friday afternoon.
If you managed to leave the rental car lot before 5 pm, you are in good shape. From there, you have two unpalatable choices to reach Dodger Stadium. If you take I-405 to I-10, expect lots of traffic. If you take I-105 to I-110, expect lots of traffic. Either way will take about 2 hours to reach Downtown on Friday 5 pm - and another ~30 minutes to get pass Downtown and get in the parking lot of Dodger Stadium.
If your rental car has Fastrak transponder, I would strongly recommend I-105 to I-110 so you can use the HOV and toll lane all the way. It will save you about 40 minutes.
If your rental car has no Fastrak transponder, I think you better have some entertainment for the kids en route. Make them go potty before leaving LAX!
Last edited by bzcat; May 4, 2016 at 5:20 pm