Sorry about your Mum OP 
Personally and contrary to popular opinion, I think BTLs are overrated as an investment for the small-scale/one man band investor, especially since the tax regime was changed so you now pay a lot more of your profit over to the taxman. In your case, if the rent would barely cover the mortgage (I assume you mean a mortgage on the BTL not on your family home?), it doesn't sound a great idea, as you would then need to be actively paying out on agents fees, maintenance, void periods, insurance and tax from your own pocket which if you only have a small income could be tricky. So unless you would be expecting very significant capital growth via an increase in house prices you'd probably not see a great return at least in the early years, and that's before we consider the active effort/stress involved in being a landlord compared to more passive investments. Also, if your family home is in roughly the same area as the BTL, you are effectively double-downing on house prices in your area - if you get massive growth you benefit twice as much of course, but if they remain static or drop you lose double. For me I prefer to spread my risk/growth a bit more than that!
It would probably be worth your while seeing a reputable independent financial adviser to take a good look at your overall financial position and your goals and risk appetite (immediate income vs long term growth for instance). They can advise best, but things to consider might be:
-Do you have a mortgage on the family home and what interest rate are you paying/how long left on the term. Might be worth paying a chunk off esp if this knocks you down into a lower LTV rate so you can get a better deal
-How is your/DH's pension situation - am guessing as a SAHM at the moment you aren't paying much if anything in? A SIPP or other personal pension might be a really good tax efficient option to consider.
-Is it worth starting a child ISA for the DC if you are hoping some of the money would benefit them e.g. as university contribution or a first car or whatever.
-Earmarking some money to retrain or start your own business might be a good idea but if you haven't yet worked out what/how/when you could stash some in an ISA or a 2 or 3 year bond so it's earning some interest in the meantime 
Hope you work it out, don't rush into anything or make any hasty decisions whilst you are still in shock/grieving...