Getting moved around? Use bolt down breakers!
Most breakers panels allow breakers to unclip and tip out. Easy dor servicing under load. Not awesome for popping out due to vibration. They also make breaker panel models where the breakers bolt down instead of snap in. And they make bolt-down kits for snap-in breakers; these are intended for backfeeds, but if you use them for normal breakers, I won't tell :)
If this tiny house gets moved more than once or twice, consider bolt-down breakers.
A "main breaker" at the subpanel is mandatory
Well not a breaker, just a shutoff switch, but everyone uses a breaker because it's cheaper. Your backfeed plan is fine and legal if you bolt it down, but you must do something to that effect.
Selective coordination is hopeless
And that is where you are going with that 29A breaker. See ThreePhaseEel's poetry for why.
It's not impossible, but it'll only work with slow trips (38A on a 30A breaker) and only on much bigger differences in trip ampacity.
Upsize the main... and the wire
10/2 makes me think you are really trying to slumlord this thing. Stop it. Even a 10/3 would be a step in the right direction, and not much more coin. At this point you have two 30A/120V feeds; inside the tinyhouse you breaker each at 15A for a better chance of local branch circuit trip. Of course this trips at the branch circuit level, so 20A+5A will trip it.
If the people in the tiny house community are telling you 10/2 and a TT30 socket, that is not wrong, but it is not right for you, given your constraints.
But you are better off still with either 6/3Cu or #1Al.
6/3 will let you breaker the feeder at 60A, and provide two legs to the tiny house. Make your local main 30A which then feeds a NEMA 14-30, which is a larger RV socket. That all but guarantees local trip first on modest overuse overloads. Inside the tiny house you have its panel with any number of breakers.
If you run 1Al you can feed breaker at 100A (or if your main breaker is 100A, lug feeds will suffice) and again with a local breaker at 30A, or 50A with a NEMA 14-50.
...Or have a power monitoring system warn you
Given the constraints you just shared, parking your tiny house at friends' homes, where you can't upservice the tinyhouse pad, you are probably better off with some sort of a power monitoring system. It would be able to warn you when you are exceedi workable load or remaining near maximum load for long enough for a breaker to possibly trip. Breaker trip curves are grossly consistent, for instance 30A for 5 minutes and 25A indefinitely are probably pretty safe on any make of breaker. You just need it to sound a buzzer as you get close,