Parental preference: Mummy do it!

[CityKity]

So my almost 2yr old has really hit the ‘mummy do it’ phase in full swing. He’ll say things like ‘daddy go away’ or ‘don’t like daddy’ and DH is really struggling with it (as am I).
Since I’ve been back at work (almost a year) DH and I alternate bedtimes and mornings, so DH is very much an equal parent and a brilliant one at that (far more fun than me). Recently (maybe the last month) DS absolutely breaks down when DH goes in in the morning instead of me. Screaming and screaming for me. It’s rubbish for everyone involved and he doesn’t calm down until he sees me and then loses it again when DH takes him back away to get ready etc.
Bedtimes have always been harder for DH, but they’ve gotten even worse with DS wailing until he can’t breathe.

So I know this is a really common issue and I have read through other threads on this, but often they have a slight dad-bashing aspect to them (DH needs to step up etc).
We both work full time and it’s not sustainable for me to be the default parent. I travel away for work every now and then, and when I’m away DS is much happier with DH, but if I’m in the house it’s a totally different story.
Will this end? What can me and DH do to deal with this?

i always used to say "no, daddy will do it today. Mummy will do it tomorrow" then walk away and let dad get on with it. Or DH used to say "no i am doing it, mummy's turn tomorrow"

And if that meant a tantrum, that led to consequences (no bedtime story usually)

Luckily my DH was completely on board and 50/50

We found that the alternating didn't work that well - it made DS1 feel like there was a choice of who did it, and he wanted to control that choice. We switched to me doing all the bedtimes for a while before DS2 was born and that worked much better as it became completely normal for me to do it instead of his other mum, and he became much more equal about which parent he preferred at other times too. Now I still do the majority of bedtimes, but DP does mornings so he gets time with both of us but we've got different roles.