Your husband has a point - though I've just read the bit about her hip operation and the cast which to be fair I think counts as extraneous circumstances!
If that weren't the case, and I had a 2 and a half year old still getting up that early, I'd be trying to take at least some measures to ensure they stayed in their room longer, even if it didn't mean they were asleep.
A few quiet toys, the bunny alarm clock where the eyes pop open when its an acceptable time to start the day, perhaps even a reward chart (I've never actually done a reward chart because I've never had to but apparently they are pretty effective for this kind of thing and this kind of age group). It wouldn't necessarily involve leaving her to cry but some pretty strong incentivisation to stay in her room quietly until at least 7am (hey why not aim for half 7!!)
At first it wouldn't mean any more sleep for you because you'd be coaching her into this, but in the long run it probably would. I dont think its too early or too young, at this age assuming no special needs or extraneous circumstances like illness or injury, it is totally possible and I've seen it be done without leaving them to cry.
But - there are different circumstances in your house at the moment and now is not the time to consider this kind of thing, by the sound of it.
Regarding your lie-in - with some partners (be it man or woman) this needs to be prearranged, mothers day or not. Today this board will be riddled with angry posts from people who didn't want this or that, just a decent sleep etc etc and at least half of them will not have even discussed their expectations with their partner. I dont know if you did or not and in an ideal world you wouldn't have to, but if you dont ask, you dont get...