I've found a few possible interpretations of these lines, each of which could make sense in the wider context of the whole poem and the emotions and attitudes behind it.
After war broke out, Edward Thomas spent a long time agonising over whether he should join the armed forces or emigrate with his family to the relative safety of America. Eventually, in July 1915, he joined the army (where he was later killed). This poem was written in December 1915, supposedly immediately after a heated argument with his father, who was more aggressively patriotic and demonised the Germans.
We can see the emotions from that argument spilling over into the poem itself: Thomas clearly rejects the conventional patriotic instincts of hating Germans and "grow[ing] hot / With love of Englishmen", which he sees as being a farce "to please newspapers". Some have even interpreted the "fat patriot" line as referring to his own father. He is distancing himself from these zealous patriots, although by the end of the poem he has established his own, different, brand of patriotism.
The choice between the cauldrons
This is a tricky one. One possible reading is that the decision is, as you guessed, between two more or less equivalent choices - that choosing between two equally attractive cauldrons is similar to choosing between two equally unattractive patriots from different countries. This is the interpretation espoused by Martyn Crucefix's analysis:
The irony is though that what emerges from these apparent alternatives (Thomas again using contrasting terms in this poem) is similar. The adjectives “clear and gay” and “beautiful” suggest that there is little to choose between these alternatives, echoing line 8 with its phrase “I have not to choose”.
An entirely different reading is that the two cauldrons symbolise the two types of English patriotism which Thomas is contemplating: the one pure and unadulterated by propaganda, the other obsessed with the country itself and opposed to all other countries. This is the interpretation espoused by Sandra Gisbert Sánchez's analysis:
He compares, in a metaphor of witches’ cauldrons, his feelings of patriotism and other patriot’s feelings. Outside one cauldron, there is his patriotism which goes beyond this hatred, so he loves the English countryside with a weather that “shall rise clear and gay”. On the other cauldron there are other traditional patriots like his father, who love England as newspapers write, also hating Germans because of the war conflict.
Honestly, neither of these interpretations is enough to properly convince me, so I lay them both before you for consideration; take or leave each one as you will.
England and her mother
Taken in the context of the rest of the poem, it seems this may be a reference to a sort of reincarnation, and that the "mother" is in fact just England herself, or an older version of the same country. Notice the reference to a "phoenix" a few lines later. If the phoenix is England, then symbolically the country is rising out of the ashes of its mother's pyre. This interpretation fits with the line that you're puzzled about, and is espoused by this blog:
Despite his distaste for discussing it, Thomas hopes for an end to the war from which ‘an England beautiful and like her mother that died yesterday’ may rise.
Another reviewer has similar thoughts about this line, as well as interpreting Thomas as one so undecided that he has no interest in picking a side (which would fit with the first interpretation mentioned above of the lines about the cauldrons):
For Thomas, England is still the mother of the land where he is from, and subsequently fights for, regardless of the careless politicians at the top, who he criticises heavily. England gives meaning to a wandering soul, lost in conflict.
I read several reviews and analyses of the poem before writing this answer: