It should be "Go to your bedroom." "Go in your bedroom" sounds wrong to my ears. (American English)

The general feature to consider and learn here is "Go to" versus "Go in" when used as an imperative. And the inflection is different because "Go to" is derogatory as is "Get in." As a result, they begin some orders. More frequently, I would say "Get in" with a younger relative if the reference were to get in (enter in order to abide/stay indefinitely in) a car rather than go to (abide/remain in) a room. And I say "Go to" much more often in superior status social situations than I do "Go in ..." Politely, I would encourage or welcome entrance away from me with "Go on in" (not "Get in"). "Go in" almost is never said in my dialect of American English in demanding reference in reference to a physical location; only objects (like a vehicle such as a truck, car, etc.). However, based on experience, I would expect some other international variant of English such as Australian, Singapore, or Indian sub-continent English to adapt and use "go in" as a command/order than my variant of English since prepositional associations with major general reference verbs (do, make, take, get, be, etc.) that turn them into particles are historically arbitrary more than they are actually locative in frames of reference.

If you want to get technical about it, no they do not mean the same thing. In the first sentence the person can go to their room but not enter. The second sentence requires the person to go into their room. HOWEVER, the 'meaning' of both is the same. If an English speaker tells another English speaker to go to their bedroom, the second person will go into their bedroom. I have no doubts about that (unless it's a child who is trying to make their parents mad by getting technical about the sentence and not doing what they are asked). The first sentence is very common (even more common: go to your room). I expect to only hear the second sentence from a person who is learning English.

I think there will be different opinions among native English speakers about whether or not both sentences have the same meaning. I personally think the second sentence should say "go into your bedroom." This is my reason why: (1) In this context when I hear the verb "go" I think there will a change of location. (2) However, "in" indicates to me that the person is already in the bedroom so there is no change in location. "In" is a preposition that indicates the location where an action is taking place, whereas "into" is a preposition that indicates the destination of an action that involves a change of location. So in my opinion the second sentence almost sounds grammatically incorrect. There is one funny meaning for the second sentence that does make sense to me. Where I live you can also use the verb "to go" and it has the meaning "to urinate" or "to pee." In this usage the verb does not indicate a change in location, so when I hear the sentence "go in your bedroom!" I am imagining a parent telling their child to urinate in their bedroom. :)

A mother telling her child: Go to your bedroom! Or Go "in" or into" your bedroom! Would mean the same thing. Said 2 different ways.