There are some great trainers out there, as with great doctors. In the same way you won't want a proctologist sorting out your cataracts, you have to make sure a trainer knows what they are doing if using one. They will need to be experienced in remedial exercise, ideally with at least a few cases similar to yours, there are many who get vertebrae fused for medical reasons, so it may not be an issue.
Money is evidently an issue, anyone who doesn't understand this needs hearty congratulations, the rest of us have been there or still are. If you have friends going to that gym you may be able to do this without a trainer if they are reliable and willing to be patient. It would be no good you training with someone like me, regardless of how good a friend, I would be too aggressive and likely to make you want to do more without even saying it. What you need is someone willing to be there as you do some very basic movements ready to take the bar off you at a moment’s notice and equally as important tell you if you are doing something wrong. Basically a friend good enough to upset you by constant correction.
The sessions would need to be very basic movements and you would have to be prepared to be doing far less than you feel capable of for some considerable time to be totally safe, something harder than you might think. You may have to modify movements to allow for lack of mobility etc. too and ensure anyone giving you hints or advise is fully aware of your condition.
An example is deadlift being switched for deadlift downs. Deadlift would mean lifting the bar from the ground, deadlift downs are starting at the top of the movement and lowering the bar as far as comfortable, not until discomfort, even if this is only a matter of inches.
I will warn you now doing the type of workout you need to do will make you feel a total prat in the gym, where others will be doing more weight over full movement. Trust me I know, having had to do it myself. It is important to do the training, but it helps to be prepared for this too. Once people know why they will give you the appropriate respect due for being committed enough to do it, but you will still feel awkward, especially at first.
Take care and good luck. Obviously let us know how you get on.