Labour putting a second referendum commitment into their manifesto might give them an edge over the Lib Dems with Remainers wanting the Tories out at all costs - but then even if Labour win power they would still have to pick a side in the referendum.
And by Labour picking a side I mean Corbyn.
In the last referendum Cameron was Remain, but his colleagues and cabinet members were allowed to campaign for whichever side they chose. Labour can also do that, but it's whichever side their leader chooses that will attract attention - and picking neither side is also a choice in itself.
As for whether the GE should happen before or after any possible referendum, there will be two weeks after Parliament returns to decide this issue. I think there's enough sway in Parliament to form a GoNU that could both delay Brexit and institute a second referendum; the leavers have now dug their position in so hard, and Boris has been such a jackass, that there's sufficient consensus amongst individual MPs on taking control. What we need to see are more Labour MPs taking a stand on the matter.
The leave campaign promised Brexit would be easy; simple to negotiate and a smooth transition out of the EU. After three years of chaos, that has been patently shown to be utter bollocks. Therefore the leavers need to defend their record in a second referendum. Their unicorn promises wont wash so well a second time round imo.