There are different thoughts on this.
Often people reduce the A time following a short nap to avoid OT
however
Reducing the A time can produce another UT nap, so the cycle repeats, and by the end of the day LO gets OT because of the missed sleep at each nap.
Tracy Hogg gave examples in her books of getting LO on a routine where by she kept LO in their room until the end of nap time even if they are awake (as you did), followed by a *full* (or close to full) A time, counted from when the nap *should have ended* rather than when it did end. This makes a monstrous long A time, at the end of which baby is really tired and likely to sleep, if they wake during the nap with OT Tracy would be there to put them back to sleep.
This is a faster method to get into a suitable routine (usually within 3 days) but we often go more slowly than this on the forums because it can be super hard work for parents. Often the slower way can still produce good, quick results, but you still need to be pretty consistent and very mindful of extending those A times, yk?
Based on what you've said I would keep her up the full A time following the short nap. You can try 2 versions of this
1. time the A from when she wakes at the short nap (if she sleeps 1hr time from WU 1hr 45 until next nap)
2. time the A from when she should have woken, when you got her up (if she sleep 1hr, lays in bed quietly another 30/45 mins then you get her up time from here - note this makes the time awake much longer 30/45 mins + A of 1hr 45 = 2hr 15 and this is what Tracy did in her examples).
Tracy also woke LOs when the routine showed the WU/E time even if they had had a disturbed sleep, wouldn't go down or OT wake ups etc, even if they had not fully rested. This again encouraged the routine into place quickly even if it did make LO tired and cranky. In effect it is following a set pattern for a number of days. You still listen to LO's needs and cues but in a more strict manner during that time. Once the routine is in place it is much easier to follow cues, allow shorter A time if you know LO had lots of stimulation that morning etc.
One more thing. At this age LO is more alert and learning about the world around her. Sleepy cues can be confusing, a yawn can now indicate she is bored of her activity and would like to do something else or that she is in the habit of going for a nap at this time. Switch the toy she is holding, read a book, sing a nursery rhyme or move to a different room or view point and see how she perks up. I think you will begin to see a subtle difference between a bored yawn and a "I really need to sleep now" yawn. When extending naps, even if the sleepy cues are there, some times we need to go by the clock a little to help LO stretch the A time and start to get better overall sleep.
Today DD woke up after napping for 1 hr but wasn't crying
If she had her full A time prior to this nap then tomorrow I would increase first A by 10 mins and sneak into her room at 50 mins to W2S.
hth
let us know how it goes