When someone dies in ohio can the property still be lived in? Also can things be removed?

If the home is truly "in her children's names" then those childrens are owners of the home and can live there: everyone on the title of a home is an owner, and just because one owner dies does not mean that the other owner(s) cannot live in the home--otherwise, whenever one spouse died, the other would have to move out.
The mother's estate as a whole must be probated, but if the home was jointly titled with the daughers, it *might* not go through probate--it depends on exactly how they were put on title (there are several ways to own property together with other people, and they are not all treated the same after one of the owners dies).
Items cannot be removed if they were owned by the mother until the estate is fully probated and settled. 
There are alot of issues here--how was the home put in the daughters' names? Who owns what in the home? How will the mother's belongings pass to the beneficiaries (presumably the daughter) and how do they get legal title to anything the mother owned which was not already jointly titled with them? Who will be the administrator or personal representative to manages the estate, and, among other things, pays the mother's final bills from any estate assets, etc.? What about any mortgage on the home--it will have to be paid, or the lender/bank will be able to foreclose. Other home expenses, like taxes, insurance, utilities, etc. still need to be paid. The daughters are strongly encouraged to retain a probate attorney to help them deal with the aftermath of thie mother's death. 
In the meantime, there is no requirement that the home be immediately locked and not entered. The best thing is for the daughters to stay in their current living arrangements, but entering the home at need to take care of it, until the lawyer helps them sort out their exact rights and what must be done.