The joke relies on knowledge of old English coinage.
A Noble was worth six shillings and eight pence, or eighty pence, which was 1/3 of a pound sterling (£), the pound being at that time worth 240 pence (in contrast with the decimalised value of 100 pence).
The coin was minted for the last time in the 1460s (and in its final years was increased in value to eight shillings and four pence, or 100 pence, in an effort to stop coins being exported to parts of Europe where the value of their gold was higher than their face value).
In its place a new coin was minted, the 'Rose Noble', also known as the 'Royal', which was worth ten shillings or 120 pence, half of a Pound Sterling.
The Noble was in production in the reign of Henry IV, going out of production and being replaced by the Royal during the first reign of Edward IV. So the introduction of the Royal, post dates the setting of the play. Whether there is a significance in that and a further layer of joke about the relative fortunes of the Houses of Lancaster and York, I'm afraid I'm too uninformed to know!
So when Hal tells the hostess to give the Noble man as much as will make him a Royal man, he is telling her to give him a shilling and eight pence and send him on his way. This would probably be perceived by the Nobleman as a great insult, though from a prince even an insult may be seen as a sort of compliment, it at least proves they know you exist. The joke also underlines the difference in rank between a prince and a nobleman.
As to his Mother, Mary de Bohun was never Queen as she died before Henry IV came to the throne, so presumably she was dead at this point. Depending on Hal's view of his mother he is telling the hostess to send the Nobleman to heaven or the devil; or perhaps to Leicester where she is buried!
