Wow, my mother-in-law problems didn't start until I had our children, your mother problems are starting already. I highly recommend the book "Boundaries" I forget the author because I have lent out my book to more and more people with this problem.
First, is the financial support to buy her time into your life, or is it a gift that she freely gives because she loves you and wants to help? All gifts are supposed to be free, with no strings attached. If this is a loan that you intend to pay her back then again, it is your money and you will pay her back so no strings attached other than you will pay her back MONEY, not your guilt. If she is expecting something in return because she is your financial savior, I highly suggest getting out from under her. Put the financial help in your court. Tell her that you appreciate the support but if it comes with strings attached, you must decline, you can't live that way. Trust me, it will only get worse. Can you get a loan from the bank? Can you change your situation at all, so you don't have to deal with her expectations.
Having your child is between you and your husband, there is no third parent, she is not a third parent and the fact that you are letting her in for a few minutes is more than generous.
You said you are trying to compromise to keep everyone happy, that is a huge mistake. We can not and never will make other humans happy. Happiness is each person's individual responsibility in their own lives. We must all come to the table already happy and then others can enhance our happiness, but we will never make everyone happy, it is not our responsibility to make others happy, so it really is futile to even try. It sounds a little to me like she already isn't a happy person and is looking to make her happiness through you two and your child.
Get that book, you will need it for way more than this first issue. My children are 9 and 8 and I have dealt with parental issues the entire time and have had many people to talk to about all our issues, and in the end it comes down to setting your boundaries to what you can and will accept as behavior from those around you. No different than an abusive person, you wouldn't accept someone hitting you, you don't accept someone trying to infringe on your space either. If you do feel guilt (you mentioned some obligation to keeping her happy since she helps you out financially) this is guilt, then you need to look into yourself and see why you feel that way, another person can not make you feel guilty, another person can bring out the guilt you feel already within yourself. So look into your life, why does this make you feel guilty, like you have some obligation to keep her happy. Maybe that is where the answer lies.
As a parent I give things to my kids because I love them and want the best for them, I do not give them gifts to buy their love. as they get older, if they need financial support, I would give because I want to help, not because I want them to see what a great person I am and that I should then be a large part in all of their lives. Put yourself in her shoes and then see how you might play things out.
Always though give respect to your mom and love, do everything in love. This is the only way relationships will stay in tact, is if everything we do comes from love for that person. Even when you have to tell someone something they don't want to hear, do it in a loving, caring about their feelings way, but not giving in to what they want because they aren't happy. This will also be useful as a parent. We should not give into what our kids want just because they throw a tantrum. In essence, that is what your mom is doing, she is throwing a mini tantrum to get you to change your decision. Don't do it, you must stick with what you said at first, otherwise you will have just taught her how to get her own way, she can throw a tantrum and you will change your mind. It is human behavior and this is how kids work as well. If a child throws a tantrum because you won't buy them the candy bar at the check out line and then you buy them it to keep them quiet, you have just taught them how to get their own way.
Sorry for the long response, hope it helps.