This is something that really peeves me off. The horse is too old now, too expensive, she needs to be somebody else's problem. Disgusting.
I understand that your family is in a tough spot financially, however things can't be too bad if you are considering rehoming this poor mare and then REPLACING her.
Hate to break it to you, younger horses can be just as expensive as older ones, sometimes more so. I have an arthritic old gelding who costs me practically nothing (hay, farrier, worming). On the other hand we have a 6 year old mare who just colicked the other night which will cost us $700-$800. The same mare who had blocked tear ducts a couple of months ago that cost us $400, also the same mare who tore up her legs a couple of months before that and cost us $300.
If money is that tight that you can't afford to care for the horses you have and you will not keep the old mare than euthanise her. It is not fair to expect a horse of that age and with "issues" to find a home that will treat her the way she deserves to be treated, especially when you are not willing to do so yourself.
Also, don't get another horse.