I have a Lenovo Thinkpad T61 with the integrated intel X3100 graphics.
I also have an advanced dock in which I can put a PCI-E graphics card.
How well will ubuntu behave when being booted up with an AMD graphics card and the proprietary drivers sometimes and then other times just with the integrated intel card?
They will both behave really well. Of course, you need to install the proprietary drivers for the AMD video card. The Intel one should get support out of the box. I would still invite you to try this questions which will help you even further along the road:
Which ATI/AMD, or Intel, or NVIDIA Graphics for Unity?
(Simple way of letting users know which one to get)
Bumblebee or Ironhide?
(In case you get a laptop with 2 video cards integrated)
How do I install the Nvidia drivers?
(Extensive answer which covers many aspects of video cards)
If you want to know which one gives less problems (Comparing Nvidia and AMD only) when installing, upgrading, changing options (Resolution, Refresh Rate, OpenGL features) and setting it up in general, the I would first go with Nvidia, then Ati.
Even though Ati is more open to the Open Source environment, Nvidia with it's proprietary driver does a great job at lowering the amount of work a user needs to install one. For many users it can be as simple as installing the proprietary drivers that come in the Ubuntu repositories. For others is as easy as adding a PPA and installing the correct driver. Same applies for Ati but Nvidia (From my experience) has had and proven to offer a better way of handling installations, configurations and has even done a great job at Bug hunting.
