had no luck with any more detail of marriage in 1878, but had a bit of a look at the family. you may already have most of this. excuse poor typing done in rush.
If William John HARRY died in 1874 and Rebecca did not remarry till 1878 have you considered the name of the father of Edith Emily died 1876 aged 3wks, Mary Ann died 1876 aged 3wks and Edith Mary died 1878 aged 6wks when Rebecca second marriage was in March 1878.
In Bendigo hospital records
23 Apr 1903 james Richards, a fruiterer age 47yrs, of view st, wesleyan
Electoral roll
1903 jas a fruiterer of view st with rebecca
1909 jas fruiterer with rebecca and jas hy
1916-1917 jas hy grocer carter with annie fruiterer and rebecca fruiterer
1919 jas hy grocer carter view st wiht rebecca fruiterer
1912-1913 there is James Richards at 492 hargreaves st a carter
there was another James richards in 1906 and 1909 but he was a traveller
1913 there was a james bloomfield Richards in Victoria st Long Gully (which is near Eaglehawk) a grocer with Daisy May
had look at some of eaglehawk cemetery
richards - norman died 1882, wm jno died 1882, wm died 1876, ella died 1897 - buried together at eaglehawk
eliz a died 1879, edwin died 1905, joseph died 1868 - buried together at eaglehawk
also at eaglehawk each seemingly buried on their own
edith mary 1878 (parents james and rebecca) age 6wks (site Mon K 160 Eaglehawk)
alice 1879 (parents george robbins and alice barrett age 57
edwin 1876 (parents robert and eliz Penberthy age 10mths
john thomas 1874 (parents john berrina & grace ellis) age 2
buried at Bendigo together
Thomas richards died 1906 age 54 (b c1852) mother eliz from VIC BDM
mary jane richards died 1914 age 63 (b c1851) parents thos joseph richards ursula clemmens from VIC BDM
Sadly in regards to baby deaths - in general it was a common practice to bury them in common ground set aside for babies.
Best of luck in your research