Samuel arrived 1833, under a 7-year sentence, so he was emancipated by 1840 which is also the year that convictism effectively ceased in NSW. He would have been free to travel anywhere, and his Certificate of Freedom has been noted by Jamjar.
I have several questions,

Perhaps you could confirm which NSW BDM documents and/or newspaper announcements are giving you family history type information to show that Mary BEAMAN nee HUMPHRIES and her sons, Samuel and Richard came to NSW? If you have the death certs (or official transcriptions) for their deaths in NSW, what answers are recorded for the question ‘how long in the colonies’…

Can you please advise the name of the ship and to which colony for Mary BEAMAN and her two children, coming to Australia in 1851 …those two lads would have been adults by then so probably manifested separately … ?

When did the chap who arrived 1833 apply for his wife and sons to come to NSW? Convictism effectively ceased to NSW in 1840.

Is it possible she and her children came as Immigrants as part of the then general Immigration Schemes that existed in the 1840s and into the 1850s?,

If so, the passenger lists usually show their NSW relatives and/or parents and at least their own native places….

So, it is possible to check what information is recorded against the two lads … I would expect it to at least note ‘mother on board’ and that father resides at …….. in NSW.
NSW Archives here:
https://www.records.nsw.gov.au/Perhaps you have the papers for

Richard BEAMAN, the labourer sequested in 1907 …

Mary BEAMAN, the widow, late of Darlinghurst and her own deceased file/probate etc 1930

Samuel Charles BEAMAN, and Hannah BEAMAN … divorce/maintenance papers in 1900
Re Samuel Charles BEAMAN,

his NSW BDM d.c. will show his parents as Samuel and Janet. He died in 1935, and the death registered Redfern. #6099. NSW BDM online index also shows at least two others by the surname BEAMAN who had parents as Samuel and Janet/Jennet.

Janet BEAMAN died in 1902, her death gives her parents as Richard and Elizabeth. #3850

And does that d.c. show her marriage, and

what name recorded for her husband, and for her children and their ages … (so, if her husband was your Samuel, then this info will not include his children by
Margaret Add, oops, Mary

my typo

).
Re Richard BEAMAN,

a chap by that name died in 1940 aged 85 at Marrickville. His death was registered Marrickville. #27216 From his D.C. where was he born, how long in the colonies/state.

Re Mary BEAMAN, nee HUMPHRIES … so there’s not just that 1930 death to consider, but I can see a burial indexed at NSWBDM for a Mary BEAMAN in 1854…. Vol 41A will be Church of England and likely there will be scant info on that Early Church Record. The index does show she was aged 52, so born circa 1802. Line 742 of Vol 41A of1854,
I will try to find spare time later this week to help further, but likely I will need some information from those questions. I have asked my husband to get out my archival boxes on my Bowman/Beaman research. The spelling variations are extensive, some caused by illiteracy, some caused by not being available for transcribing until the mid-20th Century, so worn through, ink bleeds, thumbed through, badly bound up, etc….
JM