Hi Suznor
The 10th Hussars at Ipswich in 1861 was only a detachment. The main force was at Norwich. They left Norwich in September 1861 for York, and left for Ireland in April 1863. Left Ireland in May 1868 moving between Aldershot, Brighton, Hounslow, Colchester and Blandford before embarking for India in January 1873.
These places are where the main force was based. Detachments could be within, say, a 50 mile radius, if the accommodation could not take all the men together, Or if they were spread out while ‘assisting the civil powers', ie acting as a police force.
In addition, about 10% of the strength could be in a separate Depot used for recruitment and training. This always stayed in the UK, and could also be with the main strength, or located on its own. To be certain where each man was you will have to look at the muster books in Kew. By the mid 1870s the muster books should record the names of the wives plus the ages of each child against the each man on the married roll. While in Kew you could look to see if his papers survive. If you cannot get to Kew Findmypast will be putting surviving papers online by 2011.
http://www.nationalarchives.gov.uk/militaryhistory/army/step4.htm If you are looking for other BMDs you should try the overseas/regimental BMDs on (say) Findmypast. The index will give the regiment, although I have found that there are a few mistakes in the regiment quoted, so if you find any Hamblins, but not under 10th Hussars, it may be worthwhile sending off for the certificate.
Civil registration of births started in Ireland in 1864 and with an uncommon name you should be able to find any Irish children.
Ken