So she's been employed for under a year, so no concern of her claiming unfair dismissal, if you do decide it won't work out with her.
As a nanny I work some days 7.30am-7pm. So hours wise it's doable for a local (say someone who lives 1/2 hour drive away or less) live-out nanny. As you will now be working from home more, it's even more a possibility as you could have a nanny work say a couple of long days and a couple of short days.
How involved is DH prepared to be? Could he be around for bedtime a few days a week, so he puts 5 year old and 3.5 to bed, whilst you sort out youngest?
Does your oldest child get on well with this nanny? She's been there 3 months, is there clear bonding or would he not really care if she wasn't there? How verbal is he... can he express his feelings about his nanny... if so, ask how he feels when she goes back to visit her family.
Finding a new nanny will take time. So that may not be that viable an option, unless you have someone in mind.
So lets assume for now that the current nanny stays... how can you make things better?
Do you have some time left on maternity leave, so you can spend some time micromanaging your nanny? If so, then micromanage the times she does not care for children... to help her get into a routine of doing chores.
I'm not the most tidy nanny. My boss is probably laughing at reading that statement! Though I do occasionally have a blitz and tidy the toy boxes or tidy up the lounge. I leave things in the sink, leave things laying around the lounge. It usually gets sorted out eventually but it could be several hours - I don't have any child-free time, especially when toddler doesn't nap during the day.
Are you a clean freak, is that part of the problem? With 3 children, you will have mess around for many many years to come. You can hope to contain that in specific rooms but if you want the place tidy all the time, then I feel that won't often be achieved without employing an army of cleaners. At present your nanny has time during the day to tidy up... that time may not be available later, assuming she will be caring for your baby more.
Concentrate on the most important things that must be done, plus the most annoying thing (as what annoys you most may be something quite minor but it's causing you most distress).
At the moment you are on maternity leave and thus have more contact with your nanny. Once you start work again, whilst being at home you will be working in some kind of home-office I presume. Thus your contact time with your nanny will be a lot less than currently. Would you agree? If you were not around your nanny so much, would the lack of small talk still be an issue?
How are things after working hours? Is she really hard to live with? Does she let you and DH have private time to yourselves - or does she plonk herself between you on the sofa and demand to control the tv remote?