A grammar expert will be able to tell you if it works for them.
However, as a first language speaker and reader, on first reading I thought they seemed alright. But that was because I was reading them as separate sentences. When I read them together they then didn't feel right to me. I think it's because the first sentence deals with the past, but the next sentence immediately jumps to how things are today. For me, it is the connecting of the two sentences together which causes the problem.
I think the second sentence works better starting with something like, "However, today's pace of of life, and........". This, makes the reader feel that things have changed since the time mentioned in the first sentence.
It also feels that it might be a "lead on sentence", if that's the right term, where the two sentences would, if rewritten, probably work better as one.
If it does not conflict with the context of what has gone on before, I would set the first sentence in the present as well:
"It's not easy being a single parent; today's pace of life, and attempts to survive with limited help from the welfare system, leave[s] little room for extra duties."
I think I have another reason the second sentence may seem odd. It doesn't need an "s" on "leaves". It's talking about two things "today's pace of life and ....limited help from the welfare system....leave little time....".
"Today's pace of life leaves little room": would work as only one thing being discussed.
The original second sentence seems quite long for what it is actually saying.
Others may give a more grammatically correct sentence, and additonal thoughts, but that is how it seems to me.
What were your thoughts about why it may not work?
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