there is very little straight forward when dealing with real estate and even less straight forward when you start involving your estate after passing. One of the first implications would be taxes. You can't just give large gifts (beyond a certain point) without incurring a tax liability. Then, you said you borrowed money from your mother for part of the down payment. It sounds like you likely have a mortgage loan on the property. If so, a change in title could invoke a due on sale clause in the mortgage loan. That would mean they would expect payment in full of the loan.
Then, your mother "gifting" her share to you, again, raises the possibility or taxes. She cannot just relinquish her interest to you without it being accounted for as a gift for her or income for you. You could cause some serious tax issues if not done with the tax implications in mind.
I understand your desire to limit your expenditures but you need to understand that a mistake now could cause a problem in the future that is much more expensive to fix, if it can be fixed at all. Sometimes there is no fixing things.
as to leaving it to your children in your will: there are often better ways of transferring the property to a person. Just one reason to consider other possibilities is: when you die, regardless of what you have written in your will, the first thing that will happen is your bills will get paid. If there isn't enough cash to do that, possessions and property starts getting sold. If it ends up the house has to be sold to pay your debts, well, the kids will not get the house. There are methods to consider that transfer the house outside of probate, that is, what happens with your estate will not affect the house.
another possible problem; if you need medicare when you get old enough; they can put a lien against your home so they can reclaim the money if there is enough value in your estate.
So, rather than looking to just remove your mother from title, you should look at what you want to end up with and weigh all of your options. Then you can make an informed decision.

