When I was very little, I am going to guess about five, my dad took my brother and I swimming and used the men's changing rooms, and I saw an adult stranger's penis. It actually did quite disturb and upset me for a while. I am obviously fine now, but it wasn't nice at the time (and we are a family who are fairly comfortable with nudity, so I had glimpsed brother and dad naked before and understood men had different bodies).
Because of the nature of men's toilets, with urinals, I don't think it's OK to take little girls in there and risk them being exposed to full frontal male nudity. It's OK if the gents is cubicle only - that's different.
I also agree that guys shouldn't be in the women's toilets unless there is absolutely no alternative.
Therefore the least worst outcome in this situation is to use the disabled loo (I understand the objections to this, but there is no ideal solution sometimes) . Obviously in many cases this doubles as a family room so that's it's exact purpose! Even when it doesn't, I think using it is the least worst option.
And demand more safe, gender neutral toilets and changing spaces, to acknowledge the fact that dads have daughters, women have sons, people have opposite sex partners who require assistance with toileting, etc etc.