We currently live in a senior mobile home park in Mesa, AZ and we have many people that go to Algadones for dental work. You are doing the right thing by asking for recommendations as that town has many dental offices. Some are extremely busy and some have no one there, not sure what that means but!!! Anyway, the people in our park have been very satisfied with a woman dentist with the last name of Castro, I can't remember her first name. The prices are much lower than here in the states. If I remember right my neighbor got a root canal and crown for around $300.
One thing you have to be prepared for is that you may have to spend more time waiting than you expected. Many times someones appointment takes longer than planned thereby pushing all others back. Also, I don't know where you will have your home base, but as with many things, they always don't go as planned. I some cases the people here in our park either had to stay overnight in Yuma or drive 4 hours back to Mesa and come back the next day or later. If everything goes good, no problem but if things get complicated the driving distance can be a headache.
I have another neighbor who had a tooth pulled at a dentist here in Mesa then decided to go to Algadones to have a partial put in. When he got there they found his pulled tooth had infection so they send him to the Purple Store (drug, booze, grocery, cigarettes store) to get some antibiotics and told him to come back in a week.
I don't mean to discourage or scare you but I think you need to know that as long as everything goes good there is no problem but when problems are encountered it can amount to a lot of travel time uless you are staying in Yuma or some place close to what ever Mexican town you decide to do business.
Once while I was waiting I was talking to a man from Laughlin and he said with all the trips he had to make he could have driven to Chicago and back.
Good luck and I'm not affraid to recommend having your dental work done in Algadones. Just make sure you use a dentist with good recommendations.