Hi Anne, 
Thank you for contacting the UVM Extension Master Gardener Helpline with your question, and I'm sorry you're having some difficulty with this persistent, biennial weed!

Queen Anne's lace is a highly adaptable, aggressive biennial that can definitely outcompete native species. While Vermont doesn't list it as an official invasive, it sure does have some of the right qualities to be considered such - and other states have already added it to their invasives lists. 

You are absolutely correct in identifying the lifecycle as biennial, and that is a key quality that makes it difficult/ a multi-year project for home gardeners to control. Further complicating things, seeds can be viable for longer, and a single plant can produce a wealth of those seeds. The plant can also adapt to its environment and stressors and alter the timing of its lifecycle to avoid being totally eliminated. 

However, unlike some other aggressive/invasive species that we see here, the plant spreads only by seeds, and not through underground rhizomes or sending out runners. This means that mowing and tilling CAN be very effective in reducing the population. It seems the research agrees that the best time to mow down QAL is when about 75% of the population has begun to flower - but before seeds are produced and "ripened" to be distributed and overwinter. 

Obviously, cultural/mechanical controls and most other methods, can take time due to the extended lifecycle of this particular plant, but patience is key. Mechanical controls can indeed be consistently effective in control of the population. I've included a link to a Michigan State guide on the plant and controlling it that you may want to review. 

In this case, the research seems to lean towards chemical controls not being overly necessary, as the mowing/cutting and pulling over time proves effective in reducing and controlling the population of Queen Anne's Lace. However, if you do wish to explore that route the resources below touch on pesticide advice. I am not qualified to make recommendations in that area, but if you do go in that direction, make sure you do research on the effects and warnings that come with any pesticide, and pay careful attention to instructions of application and use. A qualified individual with a pesticide application license can also advise in this case. 

I hope this helps! 

Best, 
Kristin

Resources: 

https://archive.lib.msu.edu/DMC/Ag.%20Ext.%202007-Chelsie/PDF/e2573.pdf

https://hort.extension.wisc.edu/articles/queen-annes-lace-daucus-carota/

https://plants.ces.ncsu.edu/plants/daucus-carota/

https://www.dnr.state.mn.us/invasives/terrestrialplants/herbaceous/queenannslace.html

Hello Anne:  Kristin has given you some excellent resources and information on controlling Queen Ann's Lace.  

I want to follow up with additional information on Queen Ann's Lace lookalikes since we do not have any images or a specimen to positively i.d. your plant. Control  methods can vary, and it is important to positively i.d. before deciding to control with a pesticide, if you choose to take that approach. Also,
when we include a link to a resource that recommends a chemical, it is only for informational purposes; the chemicals may not be registered for use in Vermont.

https://extension.illinois.edu/blogs/know-how-know-more/2017-06-20-watch-out-queen-annes-lace-look-alikes