Hi again!
Sounds like 1.75 hrs was about right A time for that first nap for now if she settled herself quite easily and showed some signs of going back to sleep (even if it was only when held) I would stick with that for a couple more days before trying another increase to see of that helps get a longer nap.
Waking after 40 mins sounds like she's not learnt to transition to the next sleep cycle. Have you tried going in to her before she wakes and holding her in the cot to try to ease her into next sleep cycle without her waking? You might need to replace soother at that point too.
Could I ask why you are looking at 1.75 A time for first nap and 2hrs for next one? It's not necessarily wrong- some LOs do have A times which increase throughout the day, but some have consistent A times.
If you get a short nap, I wouldn't go for an A time longer than 1.75, and she may need a slightly shorter one. Some babies need shorter A times after short naps, some cope with the same A time but usually not a longer one.
I understand the trouble with resettling when you have another older child around. I used to have to just accept short naps from DD at this age & adjust rest of day around them, if she hadn't resettled with 10 mins or so...or by the time my toddler came into the room, bathed it in light and started talking and singing to the baby!