The relationship with your client is totally irrelevant
Where and when you get paid is totally irrelevant
Whether you own or do not own your own business is totally irrelevant
Whether the client is paying you, or your business, is totally irrelevant
Whether the company is a US company or a foreign company is irrelevant (it's quite common to meet, say, your Japanese client in the US for some reason)
The ONLY THING that is relevant is this:
If you are there for MEETINGS
you are totally OK. That is the very purpose of the visa.
If you are there for "work"
you cannot do that.
That's all there is to it.
Thus you literally said:
Purpose of this trip is to attend meetings and work there for the duration of my stay.
If on arrival you say the words "I'm here to work for two weeks" the officer will roll his eyes, mumble "why did you say that" and send you home to Europe.
If on arrival you say the words "I'm here to meet my client Massive Engineering for a couple weeks" he'll just wave you in, like the other 60% of people on the plane in the identical situation.
That's the deal.
Note that anyone who has actually done this (and vast numbers of folks do) will explain this to you. For example, see the excellent example by @brahms in the comments.
Yes, in reality you'll probably do some "work" while you're there. 100.000% of people do this. It's not as if you will sit there and say "I can't open my laptop and do one line of code". In fact, you actually can't open your laptop and do one line of code, as that is "work", by the letter. But the reality is everyone does that. If you're only talking a couple weeks now and then, that's how it goes down.