Have you considered moving? A reliable caring nanny who is dependable is hard to find. You are in a one bedroom apartment now. I would think sooner rather than later you are going to want the baby to have their own room. An apartment with an elevator would make you life easier too.
I would assume that if her knees are really bad she also can't get up and down on the floor very well and the baby is only going to be getting heavier and heavier. I think you're going to have more of a problem as you baby gets older this year and she's playing on the floor all the time. Then your next worries will be what if she can't run after her at the park or a store when she bolts (like all mobile babies/toddlers will do).
If this isn't a good long term fit the time for a change is now before really strong bonds are formed and you will also have more time for appropriate notice.
She's clearly made up her mind. That's fine but it seems like she's looking for excuses to make it this woman's fault.
It's wrong to say this woman bullied and took advantage of her.
I don't understand how inability of handle big, heavy stoller on the stair means she won't be able to get the baby out of the apartment if there's an emergency. There are threads here all the time about how difficult it is to get big strollers on and off Disney buses. When does that ever mean someone can't manuever with their baby?
She didn't immediately know how to fold the stroller or put the cold weather cover on? That makes her incompetent?
It sounds like the Op doesn't think this woman is a good fit. That's her prerogative but don't blame the nanny to make yourself feel better.
To the posters who have said this might be more "about the OP" than the nanny: So what if it is? It should be about her and her child. Also, PPD, even when successfully treated is usually present for at least a year. So the best thing she can do in this area is mitigate any issues she has with her child's care. Not to do so would threaten any sense of well-being and the healing process.
BIG HUGS, OP. You are a good mom and are advocating for your child. Take care of yourself.

I thought that the bold part was really interesting. You say "we went in a cab". If she couldn't figure out how to fold up the stroller and put it in the cab, why didn't you hop out and help her fold it and get it in the cab? It just seems strange that the cab driver had to get out and come around from the driver seat to help her fold it, but maybe I'm missing something. Stroller manufacturers are constantly coming up with new tricks and techniques to fold up strollers. I've used several different strollers, and all of them seem to have a different trick to fold it. Perhaps she wasn't as skilled with folding your stroller, especially if it is a newer stroller, as others she is more familiar with.
That being said, if there is something that seems "off", I would give her notice and find a new nanny. Sometimes you have to interview and get to know several babysitters and nannies before you find one that is right for your family.
I am curious....if she can not lower the stroller down the steps WHERE is the baby when she is getting help from doorman to lower the stroller?
I think if THIS gives her trouble, as baby grows and becomes a active toddler there will be more issues
Also, it is strange because on another board I frequent, there was a post from someone saying that everyday they watch the nanny next door taking the child outside in a stroller, and that the nanny doesn't seem to be able to maneuver the stroller down the stairs in a safe way. He said it is an accident waiting to happen and he didn't know if he should tell his neighbour what was going on. Poor guy got berated for watching this unfold every day without going out and helping and/or being told to mind his own business. I wonder what ever happened with that one! Could he be one of your neighbours lol?
Yeah I think OP is really reaching for excuses here...you don't like her political beliefs? Not knowing how to fold up the stroller the first time? I also don't think you should resent her because YOU made a quick decision. Not her fault. She sounds like a good nanny but one that you just really don't want, so for the sake of everyone I would think its best if you let her go. But I think you should listen to your husband's view too, maybe he is afraid you are being rash again and in another few months when you have possibly gone from the frying pan into the fire (finding good child care is no picnic) you will regret letting her go and want her back??
That was my first thought.
OP, if you're concerned about the political leanings of your caregiver, then you are clearly hoping she lasts longer than the baby phase. How do you think she's going to be at chasing a busy toddler? If this is your first, maybe you don't understand yet how physically taxing that can be. At the very least, you're going to want someone who can get down on the floor and play with your toddler.
It's the same stroller that everyone in the neighborhood has - yes it's on the bigger side but it's bot so complicated that the cabbie couldn't figure it out in less than 30 seconds.
I do get the point about overstepping and I think that's fair and a good topic to revisit.
Still doesn't solve the physical difficulty.
Or the fact that for whatever reason I'm not in love with her. I think it's a combination of the physical part, the fact that she said she could do something she couldn't, the fact that the baby is now stuck inside unless she has help getting her out, the fact that I felt "forced" to hire her when i was in a bad place mentally, the fact that she's more conservative in her beliefs about certain subjects than I am...it all adds up for me.
I agree that everything EXCEPT the mobility issue is a non issue. The rest, just things to justify your decision (and there is nothing wrong with your decision to need justifying).
Political views are not something that should even be discussed much less a concern. So she is homophobic? Do you really expect her to have these kinds of discussions with your child? Not being able to fold a stroller---I have raised 3 children and ran a child care center for 12 years and I still can't fold dgd's stroller that isn't something that you just "know" because you are in the business. All of these are nitpicking like your husband said. But that doesn't mean you don't have reason to be concerned about the lady's mobility. Just make sure you make a more informed decision with the next one.
You have basically made up your mind to get rid of her but before you jump in and hire someone else that you may not like in 3 months can I make a few suggestions?
You and your dh should sit down and write down all the things that are important to you that the nanny do in her daily care of your child. Get on the floor, go outside, etc. etc. List these in order of importance and make sure you are on the same page with your dh. Decide what things are deal breakers. If not being able to get the baby and stroller down the stairs easily is a deal breaker then ANY nanny needs to know that up front. Don't just hire the next one. Take a few days off and be at home while she cares for your child and see how she does in her day to day routine. Let this be a trial period.
And let me just add, NO ONE is going to be able to replace you and your loving care of your child. If you are feeling any guilt about working, you will NEVER be able to find someone to care for your child that makes you 100% happy with them. Just not going to happen. You need to be absolutely positive that you can push any guilt or jealousy to the side and pick someone to care for your child otherwise you are going to be changing nannies every few months and that is not good for your child.
...And let me just add, NO ONE is going to be able to replace you and your loving care of your child. If you are feeling any guilt about working, you will NEVER be able to find someone to care for your child that makes you 100% happy with them. Just not going to happen. You need to be absolutely positive that you can push any guilt or jealousy to the side and pick someone to care for your child otherwise you are going to be changing nannies every few months and that is not good for your child.
Good one - very thought provoking.Politics should not play apart in hiring.
I just wanted to add, that I went out of my way for my kids to be around all different cultures, economic status and politics - it was a great way to teach critical thinking and show my children that people of different backgrounds are great people.