Answer: The baby poplars are probably coming up from the roots of the old tree. You can try spot treating them with an herbicide containing glyphosate, read and follow the label directions. Between that and constantly cutting them down, the root will eventually become exhausted.
Moles are in some ways beneficial to the soil, so they do not need to be controlled unless they are causing a dangerous situation by tunneling. Moles do not damage plant roots. (Voles eat plant roots.) Moles eat insects, grubs, slugs, earthworms and so on and their presence indicates a healthy soil. There are many (ineffective) home remedies for moles. You may find the following information more helpful if you do need to control them.
I hope this helps!
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