A little help?

We know that I applied to lots of companies asking to intern with them yes? We know that only Designer Lady got back to me yes?
Well.
On Monday a huge london based PR agency emailed asking what my availability was with regard to interning with them.
I froze .. all these ideas filled my head of whether I could do 2 internships at once, whether it'd be sneaky, whether it's considered rude, whether I could handle 2 work loads, whether I'd be walking away from a big opportunity if I turned the agency down..

I replied saying that I worked part time for a designer and could only do 2-3 days a week, expecting the agency to be uninterested.. They wrote back confirming my thoughts, saying they really preferred interns to be full time.

End of story yes?

No.

Either my CV & covering letter to this agency were uhhhmazing, or they're desperate for interns (more likely the latter) but they emailed again today.

'Hi, what days part time are you available? Just trying to work out a timetable that may work.'

So now I'm in this awkward position where I have no idea what to do. This is a great company to have on my CV, but I do want to keep working for D-L (Designer-Lady).. I don't want to tell D-L that I want to work somewhere else, only to be dropped by her, treated like crap and not learn anything at big agency.. but then I do think I could do both.. It's a pretty sensitive situation - I appeal to you, dear reader.. What do I do??!