If i did plug it in would the 20amp be stepped down to 15 amp or would it cause a problem to the mh circuity?
No, it will not hurt the motorhome. and no, it will not "step down" the amps.
The outlet doesn't push amps into the RV - the RV sucks out whatever amps it needs, and that is governed by what appliances you use. The limit on what the RV can get from the outlet is governed by the circuit breaker, which presumably is 20A for those outlets. The dogbone you have, however, has wires large enough to handle only 15A without possibly overheating. Therefore you should restrict your power needs to 15A or less when using it. If you use the full 20A that is available, odds are the dogbone will get hot and, after awhile, melt the plastic around the plug. Not a good thing, but probably not damaging to the RV either..
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL