OP, is this coming from you or is this coming from your mum?
I find it easier to believe she is offering to buy you a house if she can kick him out if you die/split up. I imagine you have banged on for years about how terrible he is with money, that will have clouded her view.
What she needs to consider is the mess she is causing.
Irrespective of whether he is shit with money or not (she should note: her child still chose to breed with him knowing this), this man has put 13 years of his life into a relationship with you including raising one child, with another one to possibly come further down the line, and cannot just be treated like a passing vagrant whom you or she choose to provide a roof for or not.
13 years of paying towards your relationship, your rent, your holidays, life. He's got skin in this game and it's horrific for you not to appropriately account for this.
Whether it's coming from you or your mum doesn't matter I guess, but the sentiment remains the same. Flaws or not, you can't treat the father of your child and a long term life partner like a one night stand you can boot out at will.
If your overriding concern is your children's inheritance, something needs to be drawn up (in the form of a will) that says he has a right to live in the house until he dies. If he sells it, it splits 33% between him and your (future two instead of one) offspring.
You say he can afford to buy his own place but you also imply he needs to be the sole worker and pay for house maintenance for five years. You say he prefers to spend. So, let's be real, if he prefers to spend, he is never going to buy his own place as a security blanket for himself.
If you make this man homeless when you die, even if the house is held for your children, do not underestimate how much your future children might resent you taking a family home away from their father.
Also, good luck with telling your lifelong partner that he has as many rights as a lodger, but with all the emotional and financial attachment of a father.
That's going to be very awkward.
I would suggest that legal papers do not need to be drawn up at all, rather a vast adjustment in attitude of your thinking about just how disposable this man seemingly is in your life.