Harlow Carr spreading??

Please be patient, I'm new to roses! I admired a nearby hedge of roses and the owner told me they were Harlow Carr. I treated myself to 5 of them last year but they've been a bit of a handful, bless em. Last year they had a lot of mildewy fungus but did flower, and am not sure they're in the right place, possibly too close to a low wall for good air circulation. I'm thinking about moving them.

Just noticed that a few of them have sent up new shoots about a foot away - what shoot I do with these wee beasties? Are they new rose bushes in the making, or just a nuisance?

Thanks in advance