It's not possible for the housekeeper to travel with them. There is no such visa available.
They need to move to Canada first. Once they have arrived in Canada, then will need to explore whether it will be possible to obtain a work permit for the housekeeper as an in-home caregiver to the children. Depending on the province, a work permit may not be immediately possible.
She needs to be eligible through the HCCP program for childcare if it is for childcare. Once you are in Canada, you set up a business number and show that you can afford a full-time caregiver with the median salary for the job (usually around $35k per year). The program is based on quotas and only opens on January 1. She needs ECA for education and IELTS. She applies with a job offer. Processing is about 3 years. So if she can apply in 2025 then expect response around 2028.
If for not taking care of children but full-time housekeeping, then they will want to settle in Canada first. Then they need to post the job on Canadian sites, and prove no one in the country can be hired. Not sure the position is even elgibile for a LMIA because in Canada, few households require full time housekeeping.
No. She cannot work for them as that would be illegal. She is a visitor and can visit up to 6 months. She needs to show her own funds (bank accounts), travel history, ties to her country of citizenship (job, property, business, investments, spouse/children).
It will likely be very difficult for her to get a TRV out of concern that she would work illegally if her current employers are PRs and moving to Canada. You should be looking for new caregiver or housekeeper in Canada. The cost of having full-time help is also substantially more in Canada so a full-time caregiver may not make sense even if you do have enough income in Canada. Most have cleaners come in weekly for a few hours or every second week if they have the extra funds while many have to cook, clean, shovel, rake, etc. themselves in Canada because labour costs are much higher than in some parts in the world. In many parts of the world it is very affordable to have many full-time workers to maintain your home. That is reserved for the very wealthy in Canada.