It doesn't matter what Botox costs. Never EVER co-sign on a loan for someone who's not your spouse. Never EVER EVER! If she won't pay her own bills now, what makes you think that she will pay on this loan? And do you know who they will come after when she stops making the payments? YOU! They will trash your credit and you will either have to live with that or pony up $3500. If you have that kind of money to give away, just give it to her and be done with it. That is, if you want her to keep acting like she's your 3rd child.
Your mom is an adult, and she really should be ashamed of herself for asking you to take on a financial obligation simply because she has been irresponsible with her money. You have two babies at home, and I really can't wrap my mind around a grandmother being perfectly willing to take money that could be used for the care and education of her grandbabies.
Besides this being something you should NEVER do, it's really not fair or right for her to put you in this position. It's hard to say no to our parents, but in this case, you have to. If you don't make her do for herself now, nothing will stop her from seeing you as an ATM the next time. And since not paying on this loan won't affect HER credit (because it's already bad or they'd give her a loan without a co-signer), she'll go on with her life and you'll be stuck with $3500 in bills that you did nothing to accumulate. IMO, that's just wrong. You have to put your husband and your children first ALWAYS. You don't have to give her a reason because you're an adult and you don't owe her any explanations for what you do with your own money. Just say no. And if she presses you, put the blame where it belongs--on the person who runs up bills she can't or won't pay.
If she throws a tantrum, it's manipulation. Again, something a mother should never do to her child. Don't play the game, and don't try to come up with a list of reasons. If she is ever going to be financially sound, she needs to learn how to get herself together and spend her money wisely. She doesn't get to spend YOURS whenever she uses up all of her own.
....LF