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It looks a lot like Creeping Cinquefoil. Here is an article that will assist you in getting rid of it:

https://www.gardeningknowhow.com/plant-problems/weeds/cinquefoil-weed-control.htm

Potentilla bloom from late summer to even early frost.
Full sun location is preferred or partial sun can be fine.
Don't fertilize your Potentilla, they may be getting too much nitrogen which will inhibit flowering.
Too much water can also be an issue, they are drought tolerant.

https://www.gardeningknowhow.com/ornamental/shrubs/potentilla/growing-potentilla-shrubs.htm

With hard to find plants like this, I have the best luck looking on sites like eBay and Etsy for sellers who are selling plants from their own gardens.

Potentilla may not be a good choice for a drought tolerant garden. They prefer a evenly moist soil.

I'm listing a few links for you that may give you more help in selecting plant species.
I always encourage you to visit local garden centers to look around and find plants that are good cultivators for you growing zone.
Fall is generally a very good time to get new planting is the ground. Follow the planting directions for each species and make sure they receive adequate water, daily for the first 2 weeks and then you can cut back.
Heavy rain can be stressful and cause the death of any plant material. Mother Nature is impossible to control. Remember that most reputable garden centers guarantee their plants for 1 year.

https://www.gardeningknowhow.com/special/xeriscape/drought-resistant-shrubs.htm
https://www.gardeningknowhow.com/special/xeriscape/drought-tolerant-plants-for-nearly-any-landscape.htm
https://www.gardeningknowhow.com/special/xeriscape/drought-tolerant-gardening-the-cheaper-landscape-alternative.htm
https://www.gardeningknowhow.com/ornamental/shrubs/potentilla/growing-potentilla-shrubs.htm

Summer blooming shrubs like this produce flowers on new growth. So if possible prune the plant before spring growth begins. Pruning for shape takes practice (and patience) but cut a little at a time shaping the plant as you desire, stepping back to see how it looks as you go. You don't want to take off too much or you'll risk losing the round shape you're trying to achieve.

Either method that you choose will be fine. This article will give you more information: https://www.gardeningknowhow.com/ornamental/shrubs/potentilla/growing-potentilla-shrubs.htm