I'd say that strictly speaking they are a bit different.
With (a), the focus is on "we have to ... now": there are many problems, and *now* someone or something is pushing/forcing you to solve them (e.g. your boss). The problems themselves may have existed for a while.
With (b), the focus is on "we have ... now": the problems just popped up. However, you're only saying that they are there and need to be solved someday; you're not necessarily going to do it right now.
Sounds like one of those exercises where you have to rearrange the jumbled words in an order that makes sense (there was another post like this just recently).
In this case, the above two arrangements are both valid. The function of "have" changes, and that gives slightly more or less weight to the timing or the volume, but in either case the meaning of the two sentences is virtually the same; we've got problems, they need to get fixed.
I'm going to assume that you are trying to say the same thing with each of these versions. In each case I would understand you perfectly and the meaning would be the same and both are correct. However, as a native speaker, I would leave out the word "that" in each case , and then version b would be the most natural for me.
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