Remove the flooring in any way you can. Since it is glued down, it's not going to be easy. (I'm not a big fan of glued down floors for the reason(s) you've mentioned.) IF, and I say IF there's an UNDERLAYMENT directly beneath the existing flooring, consider taking that up too. Because, under that is probably the sub-floor. The sub-floor is smooth, and after you've removed what you can, you MAY have to add a NEW layer of underlayment. W/O knowing the 'layers' of your ENTIRE floor, it's hard to say if you'll need an underlayment first before you install your new floor.
If you're left with the existing floor being glued DIRECTLY to the sub-floor, you're gonna have more 'issues'. You can try to SMOOTH out the 'residue', but that could be hard. Or, you could install a NEW layer of, say ..., 1/4" underlayment before your new floor goes down. The downside to this is it RAISES up EVERYTHING that the floor comes in contact with. Closet doors, entry doors, stairs, baseboard trim, other rooms, and so on. It may cause NEW problems. You want to keep this in mind even if you have a Pro do the work. I would suggest that if you aren't sure of what's going on, or are at an 'end', ctc. a Pro for advice. At times, it's the best thing to do.