Unfortunately as it's legal, it's really his call.
The bubble bum booster is a good idea. It's very narrow and it would raise her up better so the seatbelt will fit better. It would be better than nothing. However the seatbelt does need to be routed properly through the belt guides, even though this is likely to be fiddly between two other car seats. Do you think DD could be shown how to do this, if your ex would take affront to being shown?
Safety wise, in the middle seat between two other seats it is not actually the end of the world (which is why it is legal), she'll have some protection from side impacts from the other seats, and although she would be much better protected in a booster seat, it's not in the same league as a child being totally unrestrained. There are two main issues with seatbelts for a child her age as I'm sure you are aware, but just to explain for the purposes of harm reduction, the first one is that the lap belt will be too high on her tummy and in an accident this could be fine but it could also cause internal bleeding, so she needs a thorough medical check over after any accident even if there is no visible injury (If I understand correctly, this is likely to happen anyway in a crash serious enough for ambulance to attend, even if all DC properly restrained). The bubble bum, or any legal booster seat where the belt guides can be used correctly, would vastly reduce the chances of this. Don't be tempted to suggest (or accept) sitting her on a loose pillow, and there are some "slim booster seats" on amazon which I'm almost certain don't actually meet the correct standard, as the belt guides are just made out of flimsy velcro straps, so watch out for those too.
The second issue is that because she will be too short for an adult seatbelt, the diagonal belt is highly likely to rub against her neck which is uncomfortable. For this reason, younger children often want to tuck it under their arm or behind them, and sometimes adults advise them to do this, believing that it is a safe way to wear the seatbelt. It is not safe to do this, the lap part of a lap-and-shoulder belt will only restrain properly if the top half is tensioned correctly by the upper body, and if it's placed under the arm then the child will move much further forward and risks head injuries as well as injuries to their ribs. So do tell her that she must keep the seatbelt on her shoulder, even if it rubs her neck. It's OK for her to put e.g. her hood between the seatbelt and her neck, or to use a fabric seatbelt cover on the top part of the seatbelt only, to make it more comfortable. However, they should not use one of the fabric triangles or clip style "belt adjusters" which wrap around both parts of the belt. The issue with these is that they pull the lap part of the belt too high up which exacerbates the issue with the seatbelt being too high and can worsen both the likelihood and severity of injuries caused by this seatbelt position, because effectively the child has the force of both parts of the seatbelt on their tummy. Unfortunately, you can buy these in Halfords etc perfectly legally which gives the impression they are safe. They make seatbelts less safe, so IMO ought to be illegal, because if you're using this product then it means that the child needs a booster seat and/or needs their booster seat adjusting correctly. There is no reason ever to use this product. It doesn't do the same job as a booster seat, and since booster seats are legally required for children aged 3-12 it doesn't make sense for it to be sold. It is safer for a child to wear a seatbelt even though the seatbelt is too big for them.
You can get 3 car seats across in a row in most standard family cars and even some small cars if you play around long enough with the right combination of seats, but I appreciate that is probably overstepping and you can't make that decision for them. Often cheaper high back boosters are the slimmer models, and these are absolutely fine, much better than nothing at all.
If they ever find themselves in the car with only one of the GF's DC, they do need a booster seat spare for DD to use as she will not be able to use the loophole in that case. It only applies if both of the other car seats are occupied.