Answer: Congratulations for sticking with your gardening, even though it can get frustrating! Tulip bulbs can be lifted and stored for the summer or replanted immediately, and the johnny jump-ups are easy to transplant, or you can save seed from them to plant later. Unfortunately, the peony and sweet peas really resent being moved. You may be able to work around them, or you may be able to improve the soil in each individual planting hole. Tilling is always a rough and disruptive and hard to control job, so could hand digging to work in additional soil amendments. If weeds are the actual problem, you can cope with most of them by mulching. Place several layers of wet newspaper down and top them with several inches of organic mulch. These suppress most weeds and also add organic matter to the soil and improve it as they break down. Any perennial weeds that emerge through the mulch layers can be cut off repeatedly, which will eventually spend their reserves and kill them.
You might also ask an experienced gardener to help you identify the weeds and flowers -- offer them lunch or dinner in trade. I hope this helps.
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