You must buy lugs either way. Do it right.
You can't double-tap a lug. You can buy "staircase" lugs that are 1-lug width but provide 2 lugs, but you can't torque one without removing the other. And they may not fit on your breaker. In that case, you'd use 3-lug Polaris connectors.
Regardless, these don't come in small-large-large, so you'll have enough for dual 200A connections.
Since you're stuck buying the lugs anyway, it's cost-neutral whether you tap the bottom or top of the main breaker (e.g. Service side or breaker-protected side). Tapping the service side is a) Very Super Mega Bad from a safety and Code POV, because it's sending power to the subpanel totally unfused, and even worse (if that's even possible) b) since the sub is main-lug, it has no protection whatsoever for the buses - another show-stopper. Other than that, Mrs. Lincoln, c) it will have worse issues with bending radius due to the smaller area there.
So "on the breaker-protected side" is the non-exploding answer.
The breaker protects the wires
Given that the cost of wire is not critical when only going a couple of feet, use wire rated for 200A, so the breaker protects this wire. (Failing to do so is a codevio).
As long as you tap the breakered side, and use 200A wire, the subpanel doesn't need a main breaker if it has 200A+ busing. Your baby panel doesn't, so it would need a 100A main breaker, plus likely another pair of 2-lug Polaris to step the 200A wire down to something that will fit on a 100A lug. Therefore, for this and so many other reasons, I recommend this baby panel go back to the store, and spend a few dollars more on a 200A-bused panel - main lug is fine.
Not least, you won't be back here going "My panel is full, what do I do now?" Spaces are cheap; regrets are expensive.
Oh, snap: 310.15(B)7
There's one other wrinkle.
Right now, all your service's wiring goes onto the mobile home via those wires. That qualifies you for an 83% friendly "De-rate" based on NEC 310.15(B)7, since NEC is basically calling this an extension of your service drop, and letting you use service-drop sized wires.
Once you split it to two different destinations, you lose your 310.15(B)7 discount. That means adding this subpanel may make your long-existing cabling to the RV too small.
First, check if that is so. If it is, this is where you'd want to throw yourself on the mercy of the local permitting authority, and ask them to "grandfather" it.
And if they won't, then you could pull the meter, replace that 200A main breaker box with a 200A main-breaker service panel (as small as you can get it), add a 150A? 175A? breaker feeding the mobile home on its existing wires. Then, this "main" panel will have gobs of extra spaces for whatever you're trying to do here.
Heck, a wise choice of panel might even make a generator interlock both feasible and affordable.