You have a few options here
Personally, I find many of the larger meter-loadcenter combinations to be wastes of space, especially in a remote-metered application like yours. You'll probably never use anywhere close to all the spaces in the MBE2040B200BTS with it mounted on the shed; furthermore, using that meter-main forecloses you from upgrading the feed to the house to 200A in the future, as a 200A breaker simply won't fit in the half-width loadcenter it provides.
With the considerations of a 3" incoming utility conduit, EUSERC approval, and provision for 200A to the house in the future in mind as we look for meter mains, this leaves us with roughly the following options:
- If you can get decent pricing on it from your local supply house, the Milbank X5169-XTL-200 provides quite a bit of flexibility in this application. It has a 12-circuit interior with a backfed 200A main breaker, leaving 8 circuits and a set of feed-through lugs available for use, while providing a single-point-of-shutoff. In addition, it has an over/under layout, which is advantageous in that it can readily fit a separate 200A breaker for the main house, unlike single-column designs, while providing a 2-pole space for future expansion once the RV breakers are taken into account.
- The B-Line U2M2RP provides a minimalist alternative here, with provisions for a 50A maximum "side" feed to the RV outlets alongside a 200A main breaker for the house. However, this does sacrifice the convenience of having a single main shutoff available to you, and also requires getting a good price from your supply house to be practical.
- A more spacious option in the "no single main shutoff" vein is the Siemens MC1212L1200SED (also known as the Murray JA1212L1200SED). This also uses an "over/under" construction, allowing the use of a 200A breaker for the house feeder, and provides up to 3 2-pole spaces for expansion purposes as well as room for the RV breakers. Again, though, this requires getting good pricing through a supply house.
- If none of the above work, and you are willing to sacrifice having a single main shutoff, then you can go with a Siemens MC0816B1200ESN. This provides an 8 space interior with a main breaker and feed-through lugs, as well as a parallel "side" feed maxing out at 50A for the shed and RV outlets, in a narrow form factor, and is available inexpensively from the usual suspects. The downside is that the remaining spaces will likely go mostly to waste in this case, but if nothing else is available, this will do.
With this, I would use a prebuilt RV outlet box such as a Midwest U041010 or equivalent. This provides a TT-30 receptacle and a 20A GFCI receptacle in a sturdy, weatherproof enclosure; you can also get a version (the U041CTL010) with a built-in panel and extra lugs to provide a feeder onward to the shed. You'll need to use a 30A and a 20A single pole breaker to provide power to the U041010 (there is also a U041, but that has a regular 20A receptacle and requires a 20A GFCI in the panel instead); if you go with the U041CTL010 instead, you can provide it with the biggest feeder your main panel will let you, up to 100A, and then use the loop-through lugs to feed the shed's panel from it, or just stick a one-pole THQL breaker in the spare slot provided and power the shed that way.
Fat conduit and fat aluminum are your friends here
You have the right idea by going with aluminum over copper for the feeder to the house; however, I would use conduit for this run instead of direct burial wire to save you the trouble of having to re-trench wires if you want to upgrade the house to 200A service. In your case, 2" Schedule 80 PVC makes good sense here, considering that you can get the run done with two wide sweeps (and a LB if the house's panel will be indoors), and that a set of 3 4/0 XHHW-2 aluminum current-carrying conductors with a 6AWG bare or insulated copper ground will fit comfortably inside it. Even if you only run a 100A feeder (2AWG hots+neutral with an 8AWG minimum ground, or a 2-2-4-6 mobile home feeder cable for that matter), you still will benefit from the oversized conduit making your pull far easier than it would in a minimum Code sized conduit. Beats having to call an electrician in with their truck of tools to rescue your over-optimistic pull job!
Go big or go home!
One other problem lurks in your plan so far: the size of panel you've chosen so far for the house. 16 spaces is a terribly small panel for anything beyond an outbuilding, considering that you can't use "double stuff" (tandem/quadplex/half-width) breakers for most residential circuits as nobody makes AFCIs in that form factor.
Instead, I would go with a 40-space or 42-space, 200A, main breaker panel for the house's main panel, as it's far cheaper to get the spaces now than to go through the labor of replacing the panel later. The main breaker is necessary because the meter-main is mounted on a separate structure (the shed), and the fact it is bigger than the feeder you want to run is of no concern to us, as all we want here is a way to turn the power on and off. This panel also will happily accommodate a future service upgrade to 200A, should you (or the next homeowner!) ever want that in the future.
If a 200A panel is absolutely out of the question for some reason, I would at least go with a 24-space or 30-space, 100A or 125A, main breaker panel instead of the rather cramped 16-space panel you are planning to use. The cost differential is peanuts here compared to the cost of adding those extra spaces down the road, still.
TORQUE ALL LUGS TO SPEC
There is one more point to raise here, and that is that you need to use an inch-pound torque wrench or torque screwdriver to torque all loadcenter and breaker lugs to the labeled torque values. This is a new Code requirement in 2017 NEC 110.14(D), and is a good idea even if your AHJ has not adopted it, as you really don't want your electrical system to develop a case of the loose lugnuts!