I have been a teacher of Couples Yoga for many years now. I really love teaching and practicing it. When I mention it to people, they often confuse couples yoga with Acro Yoga. It is not Acro Yoga nor does it offer the same effects.
Acro yoga is similar in that you have two people doing yoga together: Acrobatic Yoga. In Acro Yoga, the person on the bottom is holding the lifted partner while they do a pose. In couples yoga, both people are doing a yoga pose. Acroyoga can be friends, lovers, or strangers practicing together in a class. The main difference is the intimacy involved in couples yoga. (and no let’s not bring up the hippie dippie talk that intimacy in friendship can be just as intimate as lovers). If you are still confused: couple’s yoga is for two lovers that have a sexual relationship (hopefully) who want to feel romance and connection. They can be male/female or a LGBT couple; monogamous or polyamorous. Couples can do acro yoga or couples yoga, but couples yoga is safer lol… no resentment from overstretched muscles or being yelled at by spouse for not being able to do a pose.
The purpose of couples yoga is to develop a deeper connection to your partner and perhaps ignite the libido. As you stretch together you melt away stress. Couples yoga has very few strength building poses. It involves nice deep stretches held for an extended time. We may warm the muscles up with some moving stretches. Doing a seated wide-legged bend while see-sawing is an example of how to warm up the muscles. It also helps to synch the partners movement and breath with one another. Being fully present in the moment, synching breathing, and making eye contact we feel closer to our partner on far deeper level than before. Troubles will disappear. Hormones will be produced. Of course, do not try this if you are in the middle of a big fight.
Some poses are more challenging. If a certain pose seems too difficult then wait for a group class/retreat to learn it or until you both advance in your yoga practice. Injuries would not make for a good connection.
An easy way to start practicing couples yoga is by doing meditation while breathing in sync. If you have difficulty sitting up straight during back-to-back meditations then both partners may want a cushion under their butt. This makes sitting straight easier. Otherwise, one partner can end up leaning back putting excessive weight on their partners back. Pressing is nice, but having to hold up 50 pounds is not. As a teacher, I notice that one partner will lean more and the other supports more. This is not ideal. It is fine to do. It is just something to think about because it can show you something about the relationship as well. Meditate for a few minutes. Many benefits can happen with your chakras in line.
Other easy things to try are simple side twists, balancing boat poses and double forward bending. Go with the flow with what feels right to do. Above all, enjoy yourselves and do not get upset if your lover is not as flexible as you are. The biggest reason I see people come to class or privates is because they have problems arguing while trying to learn this new thing alone. Practice patience and do not be afraid to step away.