If you become an instructor you will lose your amateur status, and that means that if you ever want to compete you'll be stuck in a very difficult position (unless you compete with your own students in Professional/Amateur events). The barriers for entry into the professional events are quite high: these are the super serious people for whom ballroom is their entire life -- they are amazingly trained, have decades of experience, have the right body type, and are incredibly fit. If you think you ever would like to compete, don't do anything now that will make you a pro.
Conversely, it is very possible to start dancing as an adult and compete in amateur events as a hobby. There are all sorts of competitions at all levels, and they are EXTREMELY inexpensive to compete in. An amateur competion -- where you dance with an amateur partner -- might only cost as little as $20 per person for all the events you can dance in. One of the most expensive amateur competitions I know of is about $300 per couple and that includes a weekend pass to the competition, your entries, workshops, and some social dance parties.
By the way, if you are teaching anywhere then you aren't supposed to be enter as the student-amateur part of a Pro/Am couple. So, you wouldn't be able to dance with your teacher anyway if you started teaching at this other studio.
I think one thing you might try is to start taking classes at a studio that encourages its students to pair up into amateur partnerships. Such studios DO exist, a number of the "independent" studios are this way, offering dancesport classes where people pair up during class and then enter local competitions.
Another thing to try, if you want to stay in the Pro/Am world, is to shop around and see what different studios have to offer and what their pricing schemes are. Try to find a studio that does not make you sign any contracts or make you book more lessons than you want to in advance. The place I've been taking lessons to for years has no contracts and it's not really possible to buy more than 10 lessons in advance. We have some great dancers at our studio, including some Europeans who were the National Champions in their home countries, and some US Rising Star winners. These people charge about $70 per lesson...some a couple of bucks more, and some a couple of bucks less.
Different teachers and studios also charge for competitions differently. A showcase might cost $1500, but that includes 10 lessons (not with one of the champions I mentioned above, though), personal hair and makeup, payment for your teachers time, a professionally produced video, a cast party, and a ticket for you to bring a guest. I don't know how that compares to what you are being asked to pay, but I threw the numbers out there so you could see them.
Some studios have various fees etc that they charge students for going to competitions with their teachers, others do not. I take from an independent teacher at an independent studio, and I pay him a reasonable per-dance fee for each dance we enter at a competition, plus our entry fees, plus my share of his admission tickets (split between all his students there) plus my share of his hotel and airfare (also split between all his students there). I've gone to some of the biggest Pro/Am competitions in the US and only spent between about $1500-$2000 for everything because I book my own hotels and airfare, split my teachers' expenses three or four ways, and usually enter 10 events plus the scholarship event for my level. Which brings me to another point: you can save money by dancing in fewer events. If your studio tells you that you MUST do a certain number of entries tell them no. I used to dance at a franchise studio that would say to me "here is your package cost, it includes X entries and Y hotel nights" and so on. Every time they'd do this I'd say "No, I'm not spending that much money. If you want me to go to this competition I will do only Z entries and will stay at my cousin's house nearby." They'd always say to me "well, let me see if I can get special permission for you to do this a la carte" and *invariably* they'd come back to me and say "okay, yes, you can do it so long as you also buy this dinner banquet ticket." See, they'd rather have SOME of my money than NONE of it, so don't let them guilt you or push you around. It's your money, it's your dancing, become an informed consumer and take care of yourself!
Where are you located? People here might be able to suggest some studios or teachers to try out.