Advice sought on Poor Law Records

[NicolaasMars]

The couple John STEWART and Emily HOUGHTON had two children:
Percy Stewart, born 14 Sept 1889 in Blythwood, Burgh of Glasgow, and
William Herbert Stewart, born 17 Oct 1890, Anderston, Burgh of Glasgow.

As is common on Scottish birth certificates, the place and date of the marriage of the parents is recorded there. However, on Percy's birth certificate this is stated as 14 Nov 1887 Liverpool, and on that of William Herbert as 19 Sept 1887 Liverpool. On neither date can I find their marriage. Family lore has it that they never married and gave fictional marriage dates.

Soon after the second birth, the couple seems to have split up. I find Emily and her two boys in the 1891 census in Stanhope Street, Toxteth Park, Lancashire. However, Emily gives her name as  Stedman, and the last name of her sons also as Stedman. Moreover, as first name Emily gives Beatrice! However, the names and the dates and place of the births of the boys fit the data given above, so I am convinced that this is her. She is a lodger.

In the 1901 and 1911 census, I find her again with her original name of Emily Stewart, still with her two sons. Emily died in 1913 in West Derby.

My question now is: does anyone of you know whether there are likely to be records of financial support to the (probably now) single mother around 1891? (I am a Dutchman, and not familiar with the Poor Law support and its documentation.) And if so, where would I be able to consult such records? Suggestions for other sources that may help to solve this long-standing enigma are very welcome, too.

Thank you for any help you may be able to give.

[Maiden Stone]

1891 census it says "husband at sea" under occupation. The name Stedman may have been a mistake by the clerk who transcribed the census return. After all, more than half the letters are correct and even in the right order. Her place of birth is very difficult to decipher. Edit. It was St. Helens.
 Emily  stated she was a widow on 1901 & 1911 census. She had lodgers in 1901.