need help on service to new detached garage
For residential applications, the NEC recommends (but doesn't require) no more than a 5% drop to the furthers outlet, with no more than 3% of drop coming from either the feeders or the branch circuit. There are a number of calculators on the web to help with figuring out voltage drop. Playing around with some, I found that you're looking at a 2.2% drop on 240V using 150' of 250 mil, and 2.6% drop using 4/0.
The other part that might come up is whether you'll be allowed to use 4/0 for 200 to the garage & #2 to the mobile home if that's what you have. NEC 310.15(B)(7) allows the use of 4/0 Al for 200 amp & #2 Al for 100 amp service on feeders to a residential panel if it's handling 100% of the load. When you're branching off to go to a subpanel that isn't using 100% of the load, you have to use Table 310.15(B)(16), which limits 4/0 Al to 180 amps, and #2 to 90 Amps. Now I've seen arguments that other articles could apply in your case causing an exception to allow you to use 310.15(B)(7). However, I've seen a lot of confusion on this. So I'd suggest talking with your inspector about it.