Old Generator is tired, 3500 watt enough for TT?

It should run it assuming nothing is wrong with the unit. First things I would do as mentioned earlier is to shut off all the other things that may be running and see if that fixes the issue.
Remember there are items we forget that run that can draw a lot of power. The hot water tank element is one make sure it is set on gas only, charger is another as it draws a lot of power and you never see that it is on, fridge a small one but make sure it is on gas setting to name a few.