### Tell him the truth, because that's what friends do

Sometimes, talking around or avoiding an issue increases trouble, rather than decreasing it. This looks to be a case of that happening. 

You said this in a comment. 
> The main thing is, the DM is a good guy, but his girlfriend is adding
> some complications to the group because he is understandably trying to
> make her enjoy the game. His plots move slower than DragonBallZ
> seasons, and *the group wants another player, who is a seasoned AL GM,
> to step in for some faster/more reliable and on point gameplay. The
> player GM'd a one-off last weekend that was fantastic*, and we want him
> to keep going. 

 1. The point of getting your group together is to have fun
 2. What was fun was the one-off you just did. What wasn't fun was that other thing. 
 3. Point out (as a group) that it is obvious to the rest of you that she's not all that into D&D. You all don't want to force her to have that kind of fun, and maybe he needs to know that you (as a group) don't feel a desire to try and persuade her to have fun in that form: a D&D game. You can't force fun like that. 
 4. Now for the payoff, in your own words, you need to tell DM somehting like this: 

 - We are all in this to have fun, and your DMing has not been fun for the understandable reason that your priority is her: we get that, she's important to you. We'll be playing the next session with the new DM, and we hope you'll join in as a player if your relationship allows. If not, also understood as relationships are important. 

 Including a thank you for stepping up to do some DMing is certainly in order. 
 5. In that event, if she accompanies him anyway, but he's a player, it no longer becomes an issue since the DM in question isn't constrained by "trying to serve two masters."
 6. Having seen a few similar dramas play out where game and relationship clash, the longer you let it fester the worse it is for your group. 

That's about as tactful a way as you can put it. By not speaking up and clearing the air, you risk falling into the unfortunate trap of "bad gaming is better than no gaming." (It isn't). 

*And the truth will set you free.* 

Good luck. For a similar but different problem that has to do with [interpersonal dynamics, you might want to take a look at this Q&A][1]. 

----------------------------

A related issue about "trying to have it both ways" when gaming and relationships collide. 

Your DM is experiencing the problem of "having it both way" by both being able to have fun by being a DM, and spending his free time with his significant other at the same time ... when she's not all into that form of free time (group fun, versus one-on-one interaction). Quite frankly, I discovered that I had to make a choice (wife in this case) when I discovered after a few tries that she just wasn't into it (it = D&D) though the kids loved it. What happened for me was that I first curtainled and then let go of D&D for ... about a decade. Why? Because relationships are important, and the marriage is the one that got priority. 


 [1]: https://rpg.stackexchange.com/a/93021/22566