It's always hard when the problem is close to home. You don't want to hurt anyone, and you don't want to make things worse... but you just want to see everything happy. The one thing that hurt me the most when my parents would argue... was knowing how miserable they were. I really just wanted to see them happy for once... Of course, the other thing you have to understand is that this is a mother and a daughter. They've spent SO long together, that eventually, things are going to add up and cause problems. As well, for your grandmother, I wouldn't be surprised if she isn't upholding to how she was raised and the like. In a sense, my grandparents are also strict like this. My own grandmother once sent me home because a sock had a small hole in it. Sometimes, it's just a matter of respect, and a 'towel on the floor' can show disrespect to her home, or otherwise carelessness.
And after a while... those little things become bigger and bigger, and suddenly, it's almost as if there's an argument every time something small happened. How can you change it? I'll be honest, there's not always much you can do. I don't know your position in these arguments, but if you have the confidence, you can always come in and try and calm it. Bring in the voice of reason and let them know that the problem can be easily fixed if someone merely picks up the towel, apologizes, and tries not to let it happen again. And you know what... sometimes it helps to let them know it upsets you. People don't always realize how their actions affect others, how a simple argument can hurt a passerby much more than it hurts the people involved. I don't know how much it will help, but it doesn't hurt to bring up every now and then.
In terms of your mother. Well, she thinks you're close? Well, if that's what she thinks, then how will she know that you feel differently if you don't tell her? Let her know that you're happy that she spends time with her boyfriend, but also let her know that ~you'd~ like to spend time with her too. If you aren't ready to say it outright just yet, why not make a plan with her? Ask her if she wants to go out on so and so day, and just make plans. This way she knows ahead of time that you'd like to 'hang out' or just spend time together. From there, you can explain to her that you really like seeing her around, and sometimes you feel that you don't see her as often. I mean... she must care about her boyfriend, and sometimes you can get caught up in that. Considering what happened with your father (of course it must have affected your mother greatly too), this may be the hope of some new life. Something good for not only her, but you too, and sometimes thoughts like that are easy to get caught up in. So much that sometimes you overlook some of the things like staying at home and having a nice meal together :).
So I really think you should talk to your mom about this one. Let her know that you aren't upset about what she's doing, but more that you'd just want to spend some more time with your mom and be close like you used to be. Again, I can't say the outcome, but you can't know until you try, right? And if you don't show someone that there's a problem, then they won't realize, right?
I wish I could have helped you out more. Hopefully things work out for the best for everyone :). Best of luck!